AP Precalculus Flashcards: Sinusoidal Functions

Study Sinusoidal Functions in AP Precalculus with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

AP Precalculus

Sinusoidal Functions

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QUESTION

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Determine the amplitude of $y = -4 \, \text{sin}(x)$ .

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ANSWER

Amplitude is the absolute value: $|-4| = 4$ .

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What this deck covers

This deck focuses on Sinusoidal Functions, giving you a quick way to review the definitions, rules, and examples that matter most for AP Precalculus.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

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Flashcard 1: Determine the amplitude of $y = -4 \, \text{sin}(x)$ .

Answer:

Amplitude is the absolute value: $|-4| = 4$ .

Flashcard 2: Find the phase shift of $y = 2 \, \text{sin}(x - \frac{\pi}{4})$ .

Answer: $\frac{\pi}{4}$ . Phase shift is the value subtracted inside the function.

Flashcard 3: What is the range of $y = 4 \, \text{sin}(x) - 2$ ?

Answer: [-6, 2]. Range is $[D-|A|, D+|A|] = [-2-4, -2+4]$ .

Flashcard 4: Calculate the period for $y = 3 \, \text{sin}(5x)$ .

Answer: $\frac{2\pi}{5}$ . Period = $\frac{2\pi}{5}$ when $B = 5$ .

Flashcard 5: Find the amplitude of $y = 7 \, \text{cos}(x) + 3$ .

Answer:

The coefficient 7 in front of cosine is the amplitude.

Flashcard 6: What is the range of $y = 4 \, \text{sin}(x) - 2$ ?

Answer: [-6, 2]. Range is $[D-|A|, D+|A|] = [-2-4, -2+4]$ .

Flashcard 7: State the maximum value of $y = 8 + 5 \, \text{sin}(x)$ .

Answer:

Maximum occurs when $\sin(x) = 1$ : $8 + 5(1) = 13$ .

Flashcard 8: Identify the phase shift for $y = \text{sin}(x + \pi)$ .

Answer: $-\pi$ . Rewrite as $\sin(x - (-\pi))$ , so phase shift is $-\pi$ .

Flashcard 9: What does the parameter $B$ affect in the function $y = A \, \text{sin}(B(x - C)) + D$ ?

Answer: Period. $B$ determines horizontal compression/stretch, affecting how often the function repeats.

Flashcard 10: Find the minimum value of $y = 2 \, \text{sin}(x) - 3$ .

Answer: -5. Minimum occurs when sine equals -1: $2(-1) - 3 = -5$ .

Flashcard 11: Determine the sinusoidal axis for $y = 3 \, \text{sin}(x) + 4$ .

Answer: $y = 4$ . The sinusoidal axis is at the vertical shift $y = 4$ .

Flashcard 12: What is the range of $y = 2 \, \text{cos}(x) - 6$ ?

Answer: $[-8, -4]$ . Range is $[-6-2, -6+2] = [-8, -4]$

Flashcard 13: Calculate the period of $y = \text{sin}(\frac{1}{2}x)$ .

Answer: $4\pi$ . Period = $\frac{2\pi}{\frac{1}{2}} = 4\pi$ .

Flashcard 14: Identify the sinusoidal axis for $y = 4 \, \text{sin}(x) - 1$ .

Answer: $y = -1$ . The sinusoidal axis is at $y = D = -1$ .

Flashcard 15: Determine the vertical shift for $y = \text{cos}(x) - 4$ .

Answer: -4. The constant term gives the vertical shift downward.

Flashcard 16: Calculate the period of $y = 2 \, \text{sin}(3x - \pi)$ .

Answer: $\frac{2\pi}{3}$ . Period = $\frac{2\pi}{3}$ when $B = 3$ .

Flashcard 17: Identify the sinusoidal axis for $y = 4 \, \text{sin}(x) - 1$ .

Answer: $y = -1$ . The sinusoidal axis is at $y = D = -1$ .

Flashcard 18: What does the parameter $D$ represent in a sinusoidal function?

Answer: Vertical shift. $D$ moves the entire graph up or down from the x-axis.

Flashcard 19: What is the general form of a sinusoidal function?

Answer: $y = A \, \text{sin}(B(x - C)) + D$ . Standard form with amplitude $A$ , frequency $B$ , phase shift $C$ , and vertical shift $D$ .

Flashcard 20: How is the period of a sinusoidal function calculated?

Answer: $\frac{2\pi}{B}$ . Period equals $\frac{2\pi}{B}$ where $B$ is the frequency parameter.

Flashcard 21: Identify the phase shift for $y = 5 \, \text{sin}(x - \frac{\pi}{6})$ .

Answer: $\frac{\pi}{6}$ . Phase shift is $\frac{\pi}{6}$ units to the right.

Flashcard 22: Find the phase shift of $y = \text{cos}(x - \frac{\pi}{2})$ .

Answer: $\frac{\pi}{2}$ . Phase shift is $\frac{\pi}{2}$ units to the right.

Flashcard 23: Determine the amplitude of $y = -2 \, \text{cos}(x)$ .

Answer:

Amplitude is the absolute value of the coefficient: $|-2| = 2$ .

Flashcard 24: What is the range of $y = -3 \, \text{sin}(x) + 2$ ?

Answer: [-1, 5]. Range is $[2-3, 2+3] = [-1, 5]$ since amplitude is 3.

Flashcard 25: What does the parameter $B$ affect in the function $y = A \, \text{sin}(B(x - C)) + D$ ?

Answer: Period. $B$ determines horizontal compression/stretch, affecting how often the function repeats.

Flashcard 26: What is the period of $y = 5 \, \text{cos}(\frac{x}{3})$ ?

Answer: $6\pi$ . Period = $\frac{2\pi}{\frac{1}{3}} = 6\pi$ .

Flashcard 27: Calculate the period of $y = 2 \, \text{sin}(3x - \pi)$ .

Answer: $\frac{2\pi}{3}$ . Period = $\frac{2\pi}{3}$ when $B = 3$ .

Flashcard 28: What is the period of $y = \text{cos}(\frac{x}{4})$ ?

Answer: $8\pi$ . Period = $\frac{2\pi}{\frac{1}{4}} = 8\pi$ .

Flashcard 29: State the maximum value of $y = 8 + 5 \, \text{sin}(x)$ .

Answer:

Maximum occurs when $\sin(x) = 1$ : $8 + 5(1) = 13$ .

Flashcard 30: What is the period of $y = \text{cos}(\frac{x}{4})$ ?

Answer: $8\pi$ . Period = $\frac{2\pi}{\frac{1}{4}} = 8\pi$ .

Flashcard 31: How is the period of a sinusoidal function calculated?

Answer: $\frac{2\pi}{B}$ . Period equals $\frac{2\pi}{B}$ where $B$ is the frequency parameter.

Flashcard 32: What is the phase shift of the function $y = A \, \text{sin}(B(x - C)) + D$ ?

Answer: $C$ . The horizontal shift is $C$ units to the right when positive.

Flashcard 33: Determine the period of $y = \text{sin}(4x)$ .

Answer: $\frac{\pi}{2}$ . Period = $\frac{2\pi}{4} = \frac{\pi}{2}$ .

Flashcard 34: Identify the amplitude of $y = 3 \, \text{cos}(2x)$ .

Answer:

The coefficient of cosine gives the amplitude.

Flashcard 35: Identify the phase shift for $y = \text{sin}(x + \pi)$ .

Answer: $-\pi$ . Rewrite as $\sin(x - (-\pi))$ , so phase shift is $-\pi$ .

Flashcard 36: What does the parameter $A$ represent in the sinusoidal function $y = A \, \text{sin}(B(x - C)) + D$ ?

Answer: Amplitude. $A$ controls the maximum distance from the sinusoidal axis.

Flashcard 37: Determine the vertical shift for $y = \text{cos}(x) - 4$ .

Answer: -4. The constant term gives the vertical shift downward.

Flashcard 38: Determine the amplitude of $y = -4 \, \text{sin}(x)$ .

Answer:

Amplitude is the absolute value: $|-4| = 4$ .

Flashcard 39: Determine the sinusoidal axis for $y = 3 \, \text{sin}(x) + 4$ .

Answer: $y = 4$ . The sinusoidal axis is at the vertical shift $y = 4$ .

Flashcard 40: What does the sinusoidal axis represent?

Answer: Average value of max and min. The horizontal line around which the function oscillates.

Flashcard 41: State the vertical shift of $y = \text{cos}(x) + 5$ .

Answer:

The constant term added to the function shifts it vertically.

Flashcard 42: Find the maximum value of $y = 3 \, \cos(x) + 1$ .

Answer:

Maximum occurs when cosine equals 1: $3(1) + 1 = 4$ .

Flashcard 43: Identify the amplitude of $y = 3 \, \text{cos}(2x)$ .

Answer:

The coefficient of cosine gives the amplitude.

Flashcard 44: Calculate the period of $y = \text{sin}(\frac{1}{2}x)$ .

Answer: $4\pi$ . Period = $\frac{2\pi}{\frac{1}{2}} = 4\pi$ .

Flashcard 45: State the vertical shift of $y = \text{cos}(x) + 5$ .

Answer:

The constant term added to the function shifts it vertically.

Flashcard 46: Find the minimum value of $y = 2 \, \text{sin}(x) - 3$ .

Answer: -5. Minimum occurs when sine equals -1: $2(-1) - 3 = -5$ .

Flashcard 47: What is the phase shift of the function $y = A \, \text{sin}(B(x - C)) + D$ ?

Answer: $C$ . The horizontal shift is $C$ units to the right when positive.

Flashcard 48: What is the phase shift of $y = 4 \, \text{cos}(x + \frac{\pi}{3})$ ?

Answer: $-\frac{\pi}{3}$ . Rewrite as $\cos(x - (-\frac{\pi}{3}))$ , so phase shift is $-\frac{\pi}{3}$ .

Flashcard 49: What is the general form of a sinusoidal function?

Answer: $y = A \, \text{sin}(B(x - C)) + D$ . Standard form with amplitude $A$ , frequency $B$ , phase shift $C$ , and vertical shift $D$ .

Flashcard 50: What is the frequency of $y = \text{cos}(\frac{x}{2})$ ?

Answer: $\frac{1}{4\pi}$ . Frequency = $\frac{B}{2\pi} = \frac{\frac{1}{2}}{2\pi} = \frac{1}{4\pi}$ .

Flashcard 51: What is the period of $y = 6 \, \text{sin}(\frac{x}{6})$ ?

Answer: $12\pi$ . Period = $\frac{2\pi}{\frac{1}{6}} = 12\pi$ .

Flashcard 52: Find the maximum value of $y = 3 \, \text{cos}(x) + 1$ .

Answer:

Maximum occurs when cosine equals 1: $3(1) + 1 = 4$ .

Flashcard 53: What does the parameter $A$ represent in the sinusoidal function $y = A \, \text{sin}(B(x - C)) + D$ ?

Answer: Amplitude. $A$ controls the maximum distance from the sinusoidal axis.

Flashcard 54: What is the period of $y = 5 \, \text{cos}(\frac{x}{3})$ ?

Answer: $6\pi$ . Period = $\frac{2\pi}{\frac{1}{3}} = 6\pi$ .

Flashcard 55: What is the range of $y = -3 \, \text{sin}(x) + 2$ ?

Answer: [-1, 5]. Range is $[2-3, 2+3] = [-1, 5]$ since amplitude is 3.

Flashcard 56: What does the parameter $D$ represent in a sinusoidal function?

Answer: Vertical shift. $D$ moves the entire graph up or down from the x-axis.

Flashcard 57: What is the period of $y = 6 \, \text{sin}(\frac{x}{6})$ ?

Answer: $12\pi$ . Period = $\frac{2\pi}{\frac{1}{6}} = 12\pi$ .

Flashcard 58: What is the equation for a sinusoidal function with amplitude 5 and period $\pi$ ?

Answer: $y = 5 \, \text{sin}(2x)$ . Amplitude 5 and period $\pi$ means $B = \frac{2\pi}{\pi} = 2$ .

Flashcard 59: Calculate the period for $y = 3 \, \text{sin}(5x)$ .

Answer: $\frac{2\pi}{5}$ . Period = $\frac{2\pi}{5}$ when $B = 5$ .

Flashcard 60: Find the maximum value of $y = 3 \, \text{sin}(x) - 2$ .

Answer:

Maximum occurs when $\sin(x) = 1$ : $3(1) - 2 = 1$ .

Flashcard 61: Determine the amplitude of $y = -2 \, \text{cos}(x)$ .

Answer:

Amplitude is the absolute value of the coefficient: $|-2| = 2$ .

Flashcard 62: Find the phase shift of $y = \text{cos}(x - \frac{\pi}{2})$ .

Answer: $\frac{\pi}{2}$ . Phase shift is $\frac{\pi}{2}$ units to the right.

Flashcard 63: Identify the phase shift for $y = 5 \, \text{sin}(x - \frac{\pi}{6})$ .

Answer: $\frac{\pi}{6}$ . Phase shift is $\frac{\pi}{6}$ units to the right.

Flashcard 64: Find the maximum value of $y = 3 \, \text{sin}(x) - 2$ .

Answer:

Maximum occurs when $\sin(x) = 1$ : $3(1) - 2 = 1$ .

Flashcard 65: Determine the period of $y = \text{sin}(4x)$ .

Answer: $\frac{\pi}{2}$ . Period = $\frac{2\pi}{4} = \frac{\pi}{2}$ .

Flashcard 66: What is the range of $y = 2 \, \text{cos}(x) - 6$ ?

Answer: [-8, -4]. Range is $[-6-2, -6+2] = [-8, -4]$ .

Flashcard 67: What is the frequency of $y = \text{cos}(\frac{x}{2})$ ?

Answer: $\frac{1}{4\pi}$ . Frequency = $\frac{B}{2\pi} = \frac{\frac{1}{2}}{2\pi} = \frac{1}{4\pi}$ .

Flashcard 68: What is the equation for a sinusoidal function with amplitude 5 and period $\pi$ ?

Answer: $y = 5 \, \text{sin}(2x)$ . Amplitude 5 and period $\pi$ means $B = \frac{2\pi}{\pi} = 2$ .

Flashcard 69: Find the phase shift of $y = 2 \, \text{sin}(x - \frac{\pi}{4})$ .

Answer: $\frac{\pi}{4}$ . Phase shift is the value subtracted inside the function.

Flashcard 70: What does the sinusoidal axis represent?

Answer: Average value of max and min. The horizontal line around which the function oscillates.

Flashcard 71: Find the amplitude of $y = 7 \, \text{cos}(x) + 3$ .

Answer:

The coefficient 7 in front of cosine is the amplitude.

Flashcard 72: What is the phase shift of $y = 4 \, \text{cos}(x + \frac{\pi}{3})$ ?

Answer: $-\frac{\pi}{3}$ . Rewrite as $\cos(x - (-\frac{\pi}{3}))$ , so phase shift is $-\frac{\pi}{3}$ .

AP Precalculus Flashcards: Sinusoidal Functions

Sinusoidal Functions

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: Determine the amplitude of y=−4 sin(x)y = -4 \, \text{sin}(x)y=−4sin(x).

Flashcard 2: Find the phase shift of y=2 sin(x−π4)y = 2 \, \text{sin}(x - \frac{\pi}{4})y=2sin(x−4π​).

Flashcard 3: What is the range of y=4 sin(x)−2y = 4 \, \text{sin}(x) - 2y=4sin(x)−2?

Flashcard 4: Calculate the period for y=3 sin(5x)y = 3 \, \text{sin}(5x)y=3sin(5x).

Flashcard 5: Find the amplitude of y=7 cos(x)+3y = 7 \, \text{cos}(x) + 3y=7cos(x)+3.

Flashcard 6: What is the range of y=4 sin(x)−2y = 4 \, \text{sin}(x) - 2y=4sin(x)−2?

Flashcard 7: State the maximum value of y=8+5 sin(x)y = 8 + 5 \, \text{sin}(x)y=8+5sin(x).

Flashcard 8: Identify the phase shift for y=sin(x+π)y = \text{sin}(x + \pi)y=sin(x+π).

Flashcard 9: What does the parameter BBB affect in the function y=A sin(B(x−C))+Dy = A \, \text{sin}(B(x - C)) + Dy=Asin(B(x−C))+D?

Flashcard 10: Find the minimum value of y=2 sin(x)−3y = 2 \, \text{sin}(x) - 3y=2sin(x)−3.

Flashcard 11: Determine the sinusoidal axis for y=3 sin(x)+4y = 3 \, \text{sin}(x) + 4y=3sin(x)+4.

Flashcard 12: What is the range of y=2 cos(x)−6y = 2 \, \text{cos}(x) - 6y=2cos(x)−6?

Flashcard 13: Calculate the period of y=sin(12x)y = \text{sin}(\frac{1}{2}x)y=sin(21​x).

Flashcard 14: Identify the sinusoidal axis for y=4 sin(x)−1y = 4 \, \text{sin}(x) - 1y=4sin(x)−1.

Flashcard 15: Determine the vertical shift for y=cos(x)−4y = \text{cos}(x) - 4y=cos(x)−4.

Flashcard 16: Calculate the period of y=2 sin(3x−π)y = 2 \, \text{sin}(3x - \pi)y=2sin(3x−π).

Flashcard 17: Identify the sinusoidal axis for y=4 sin(x)−1y = 4 \, \text{sin}(x) - 1y=4sin(x)−1.

Flashcard 18: What does the parameter DDD represent in a sinusoidal function?

Flashcard 19: What is the general form of a sinusoidal function?

Flashcard 20: How is the period of a sinusoidal function calculated?

Flashcard 21: Identify the phase shift for y=5 sin(x−π6)y = 5 \, \text{sin}(x - \frac{\pi}{6})y=5sin(x−6π​).

Flashcard 22: Find the phase shift of y=cos(x−π2)y = \text{cos}(x - \frac{\pi}{2})y=cos(x−2π​).

Flashcard 23: Determine the amplitude of y=−2 cos(x)y = -2 \, \text{cos}(x)y=−2cos(x).

Flashcard 24: What is the range of y=−3 sin(x)+2y = -3 \, \text{sin}(x) + 2y=−3sin(x)+2?

Flashcard 25: What does the parameter BBB affect in the function y=A sin(B(x−C))+Dy = A \, \text{sin}(B(x - C)) + Dy=Asin(B(x−C))+D?

Flashcard 26: What is the period of y=5 cos(x3)y = 5 \, \text{cos}(\frac{x}{3})y=5cos(3x​)?

Flashcard 27: Calculate the period of y=2 sin(3x−π)y = 2 \, \text{sin}(3x - \pi)y=2sin(3x−π).

Flashcard 28: What is the period of y=cos(x4)y = \text{cos}(\frac{x}{4})y=cos(4x​)?

Flashcard 29: State the maximum value of y=8+5 sin(x)y = 8 + 5 \, \text{sin}(x)y=8+5sin(x).

Flashcard 30: What is the period of y=cos(x4)y = \text{cos}(\frac{x}{4})y=cos(4x​)?

Flashcard 31: How is the period of a sinusoidal function calculated?

Flashcard 32: What is the phase shift of the function y=A sin(B(x−C))+Dy = A \, \text{sin}(B(x - C)) + Dy=Asin(B(x−C))+D?

Flashcard 33: Determine the period of y=sin(4x)y = \text{sin}(4x)y=sin(4x).

Flashcard 34: Identify the amplitude of y=3 cos(2x)y = 3 \, \text{cos}(2x)y=3cos(2x).

Flashcard 35: Identify the phase shift for y=sin(x+π)y = \text{sin}(x + \pi)y=sin(x+π).

Flashcard 36: What does the parameter AAA represent in the sinusoidal function y=A sin(B(x−C))+Dy = A \, \text{sin}(B(x - C)) + Dy=Asin(B(x−C))+D?

Flashcard 37: Determine the vertical shift for y=cos(x)−4y = \text{cos}(x) - 4y=cos(x)−4.

Flashcard 38: Determine the amplitude of y=−4 sin(x)y = -4 \, \text{sin}(x)y=−4sin(x).

Flashcard 39: Determine the sinusoidal axis for y=3 sin(x)+4y = 3 \, \text{sin}(x) + 4y=3sin(x)+4.

Flashcard 40: What does the sinusoidal axis represent?

Flashcard 41: State the vertical shift of y=cos(x)+5y = \text{cos}(x) + 5y=cos(x)+5.

Flashcard 42: Find the maximum value of y=3 cos⁡(x)+1y = 3 \, \cos(x) + 1y=3cos(x)+1.

Flashcard 43: Identify the amplitude of y=3 cos(2x)y = 3 \, \text{cos}(2x)y=3cos(2x).

Flashcard 44: Calculate the period of y=sin(12x)y = \text{sin}(\frac{1}{2}x)y=sin(21​x).

Flashcard 45: State the vertical shift of y=cos(x)+5y = \text{cos}(x) + 5y=cos(x)+5.

Flashcard 46: Find the minimum value of y=2 sin(x)−3y = 2 \, \text{sin}(x) - 3y=2sin(x)−3.

Flashcard 47: What is the phase shift of the function y=A sin(B(x−C))+Dy = A \, \text{sin}(B(x - C)) + Dy=Asin(B(x−C))+D?

Flashcard 48: What is the phase shift of y=4 cos(x+π3)y = 4 \, \text{cos}(x + \frac{\pi}{3})y=4cos(x+3π​)?

Flashcard 49: What is the general form of a sinusoidal function?

Flashcard 50: What is the frequency of y=cos(x2)y = \text{cos}(\frac{x}{2})y=cos(2x​)?

Flashcard 51: What is the period of y=6 sin(x6)y = 6 \, \text{sin}(\frac{x}{6})y=6sin(6x​)?

Flashcard 52: Find the maximum value of y=3 cos(x)+1y = 3 \, \text{cos}(x) + 1y=3cos(x)+1.

Flashcard 53: What does the parameter AAA represent in the sinusoidal function y=A sin(B(x−C))+Dy = A \, \text{sin}(B(x - C)) + Dy=Asin(B(x−C))+D?

Flashcard 54: What is the period of y=5 cos(x3)y = 5 \, \text{cos}(\frac{x}{3})y=5cos(3x​)?

Flashcard 55: What is the range of y=−3 sin(x)+2y = -3 \, \text{sin}(x) + 2y=−3sin(x)+2?

Flashcard 56: What does the parameter DDD represent in a sinusoidal function?

Flashcard 57: What is the period of y=6 sin(x6)y = 6 \, \text{sin}(\frac{x}{6})y=6sin(6x​)?

Flashcard 58: What is the equation for a sinusoidal function with amplitude 5 and period π\piπ?

Flashcard 59: Calculate the period for y=3 sin(5x)y = 3 \, \text{sin}(5x)y=3sin(5x).

Flashcard 60: Find the maximum value of y=3 sin(x)−2y = 3 \, \text{sin}(x) - 2y=3sin(x)−2.

Flashcard 61: Determine the amplitude of y=−2 cos(x)y = -2 \, \text{cos}(x)y=−2cos(x).

Flashcard 62: Find the phase shift of y=cos(x−π2)y = \text{cos}(x - \frac{\pi}{2})y=cos(x−2π​).

Flashcard 63: Identify the phase shift for y=5 sin(x−π6)y = 5 \, \text{sin}(x - \frac{\pi}{6})y=5sin(x−6π​).

Flashcard 64: Find the maximum value of y=3 sin(x)−2y = 3 \, \text{sin}(x) - 2y=3sin(x)−2.

Flashcard 65: Determine the period of y=sin(4x)y = \text{sin}(4x)y=sin(4x).

Flashcard 66: What is the range of y=2 cos(x)−6y = 2 \, \text{cos}(x) - 6y=2cos(x)−6?

Flashcard 67: What is the frequency of y=cos(x2)y = \text{cos}(\frac{x}{2})y=cos(2x​)?

Flashcard 68: What is the equation for a sinusoidal function with amplitude 5 and period π\piπ?

Flashcard 69: Find the phase shift of y=2 sin(x−π4)y = 2 \, \text{sin}(x - \frac{\pi}{4})y=2sin(x−4π​).

Flashcard 70: What does the sinusoidal axis represent?

Flashcard 71: Find the amplitude of y=7 cos(x)+3y = 7 \, \text{cos}(x) + 3y=7cos(x)+3.

Flashcard 72: What is the phase shift of y=4 cos(x+π3)y = 4 \, \text{cos}(x + \frac{\pi}{3})y=4cos(x+3π​)?

Flashcard 1: Determine the amplitude of $y = -4 \, \text{sin}(x)$ .

Flashcard 2: Find the phase shift of $y = 2 \, \text{sin}(x - \frac{\pi}{4})$ .

Flashcard 3: What is the range of $y = 4 \, \text{sin}(x) - 2$ ?

Flashcard 4: Calculate the period for $y = 3 \, \text{sin}(5x)$ .

Flashcard 5: Find the amplitude of $y = 7 \, \text{cos}(x) + 3$ .

Flashcard 6: What is the range of $y = 4 \, \text{sin}(x) - 2$ ?

Flashcard 7: State the maximum value of $y = 8 + 5 \, \text{sin}(x)$ .

Flashcard 8: Identify the phase shift for $y = \text{sin}(x + \pi)$ .

Flashcard 9: What does the parameter $B$ affect in the function $y = A \, \text{sin}(B(x - C)) + D$ ?

Flashcard 10: Find the minimum value of $y = 2 \, \text{sin}(x) - 3$ .

Flashcard 11: Determine the sinusoidal axis for $y = 3 \, \text{sin}(x) + 4$ .

Flashcard 12: What is the range of $y = 2 \, \text{cos}(x) - 6$ ?

Flashcard 13: Calculate the period of $y = \text{sin}(\frac{1}{2}x)$ .

Flashcard 14: Identify the sinusoidal axis for $y = 4 \, \text{sin}(x) - 1$ .

Flashcard 15: Determine the vertical shift for $y = \text{cos}(x) - 4$ .

Flashcard 16: Calculate the period of $y = 2 \, \text{sin}(3x - \pi)$ .

Flashcard 17: Identify the sinusoidal axis for $y = 4 \, \text{sin}(x) - 1$ .

Flashcard 18: What does the parameter $D$ represent in a sinusoidal function?

Flashcard 21: Identify the phase shift for $y = 5 \, \text{sin}(x - \frac{\pi}{6})$ .

Flashcard 22: Find the phase shift of $y = \text{cos}(x - \frac{\pi}{2})$ .

Flashcard 23: Determine the amplitude of $y = -2 \, \text{cos}(x)$ .

Flashcard 24: What is the range of $y = -3 \, \text{sin}(x) + 2$ ?

Flashcard 25: What does the parameter $B$ affect in the function $y = A \, \text{sin}(B(x - C)) + D$ ?

Flashcard 26: What is the period of $y = 5 \, \text{cos}(\frac{x}{3})$ ?

Flashcard 27: Calculate the period of $y = 2 \, \text{sin}(3x - \pi)$ .

Flashcard 28: What is the period of $y = \text{cos}(\frac{x}{4})$ ?

Flashcard 29: State the maximum value of $y = 8 + 5 \, \text{sin}(x)$ .

Flashcard 30: What is the period of $y = \text{cos}(\frac{x}{4})$ ?

Flashcard 32: What is the phase shift of the function $y = A \, \text{sin}(B(x - C)) + D$ ?

Flashcard 33: Determine the period of $y = \text{sin}(4x)$ .

Flashcard 34: Identify the amplitude of $y = 3 \, \text{cos}(2x)$ .

Flashcard 35: Identify the phase shift for $y = \text{sin}(x + \pi)$ .

Flashcard 36: What does the parameter $A$ represent in the sinusoidal function $y = A \, \text{sin}(B(x - C)) + D$ ?

Flashcard 37: Determine the vertical shift for $y = \text{cos}(x) - 4$ .

Flashcard 38: Determine the amplitude of $y = -4 \, \text{sin}(x)$ .

Flashcard 39: Determine the sinusoidal axis for $y = 3 \, \text{sin}(x) + 4$ .

Flashcard 41: State the vertical shift of $y = \text{cos}(x) + 5$ .

Flashcard 42: Find the maximum value of $y = 3 \, \cos(x) + 1$ .

Flashcard 43: Identify the amplitude of $y = 3 \, \text{cos}(2x)$ .

Flashcard 44: Calculate the period of $y = \text{sin}(\frac{1}{2}x)$ .

Flashcard 45: State the vertical shift of $y = \text{cos}(x) + 5$ .

Flashcard 46: Find the minimum value of $y = 2 \, \text{sin}(x) - 3$ .

Flashcard 47: What is the phase shift of the function $y = A \, \text{sin}(B(x - C)) + D$ ?

Flashcard 48: What is the phase shift of $y = 4 \, \text{cos}(x + \frac{\pi}{3})$ ?

Flashcard 50: What is the frequency of $y = \text{cos}(\frac{x}{2})$ ?

Flashcard 51: What is the period of $y = 6 \, \text{sin}(\frac{x}{6})$ ?

Flashcard 52: Find the maximum value of $y = 3 \, \text{cos}(x) + 1$ .

Flashcard 53: What does the parameter $A$ represent in the sinusoidal function $y = A \, \text{sin}(B(x - C)) + D$ ?

Flashcard 54: What is the period of $y = 5 \, \text{cos}(\frac{x}{3})$ ?

Flashcard 55: What is the range of $y = -3 \, \text{sin}(x) + 2$ ?

Flashcard 56: What does the parameter $D$ represent in a sinusoidal function?

Flashcard 57: What is the period of $y = 6 \, \text{sin}(\frac{x}{6})$ ?

Flashcard 58: What is the equation for a sinusoidal function with amplitude 5 and period $\pi$ ?

Flashcard 59: Calculate the period for $y = 3 \, \text{sin}(5x)$ .

Flashcard 60: Find the maximum value of $y = 3 \, \text{sin}(x) - 2$ .

Flashcard 61: Determine the amplitude of $y = -2 \, \text{cos}(x)$ .

Flashcard 62: Find the phase shift of $y = \text{cos}(x - \frac{\pi}{2})$ .

Flashcard 63: Identify the phase shift for $y = 5 \, \text{sin}(x - \frac{\pi}{6})$ .

Flashcard 64: Find the maximum value of $y = 3 \, \text{sin}(x) - 2$ .

Flashcard 65: Determine the period of $y = \text{sin}(4x)$ .

Flashcard 66: What is the range of $y = 2 \, \text{cos}(x) - 6$ ?

Flashcard 67: What is the frequency of $y = \text{cos}(\frac{x}{2})$ ?

Flashcard 68: What is the equation for a sinusoidal function with amplitude 5 and period $\pi$ ?

Flashcard 69: Find the phase shift of $y = 2 \, \text{sin}(x - \frac{\pi}{4})$ .

Flashcard 71: Find the amplitude of $y = 7 \, \text{cos}(x) + 3$ .

Flashcard 72: What is the phase shift of $y = 4 \, \text{cos}(x + \frac{\pi}{3})$ ?