AP Precalculus Flashcards: Sinusoidal Function Context And Data Modeling

What this deck covers

This deck focuses on Sinusoidal Function Context And Data Modeling, 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.

Flashcard 1: What is the frequency of $y = 6 \cos(7x)$?

Answer: Frequency = $\frac{7}{2\pi}$. Frequency = $\frac{B}{2\pi}$ where B=7.

Flashcard 2: State the phase shift of the function $y = \text{sin}(3x - \text{π})$.

Answer: Phase shift = $\frac{\text{π}}{3}$. Phase shift = $\frac{C}{B}$ where C=$\pi$ and B=3.

Flashcard 3: Calculate the phase shift for $y = \text{sin}(x + \frac{\text{π}}{3})$.

Answer: Phase shift = $-\frac{\text{π}}{3}$. For $\sin(x+C)$, phase shift = $-C$.

Flashcard 4: Determine the period of $y = 3 \sin(5x) - 2$.

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

Flashcard 5: What is the period of $y = \text{sin}(x)$?

Answer: Period = $2\text{π}$. Standard sine and cosine functions complete one cycle in $2\pi$.

Flashcard 6: Determine the period of $y = 3 \text{sin}(5x) - 2$.

Answer: Period = $\frac{2\text{π}}{5}$. Period = $\frac{2\pi}{|B|}$ where B=5.

Flashcard 7: What is the frequency of a function with period $2\text{π}$?

Answer: Frequency = $\frac{1}{2\text{π}}$. Frequency is the reciprocal of period.

Flashcard 8: Identify the phase shift of $y = 8 \text{cos}(x - \frac{\text{π}}{4})$.

Answer: Phase shift = $\frac{\text{π}}{4}$. Phase shift = C when in the form $(x-C)$.

Flashcard 9: Identify the vertical shift in $y = 3 \text{cos}(x) + 5$.

Answer: Vertical shift = 5. D value shows vertical displacement from x-axis.

Flashcard 10: Find the midline of $y = 2 \text{sin}(x) + 3$.

Answer: Midline = $y = 3$. Midline is determined by the vertical shift D.

Flashcard 11: Convert $180^\text{o}$ to radians.

Answer: $\text{π}$. $180° \times \frac{\pi}{180} = \pi$ radians.

Flashcard 12: What is the frequency of $y = \text{sin}(3x)$?

Answer: Frequency = $\frac{3}{2\text{π}}$. Frequency = $\frac{B}{2\pi}$ where B=3.

Flashcard 13: What is the period of $y = \text{cos}(x)$?

Answer: Period = $2\text{π}$. Basic cosine has the same period as basic sine.

Flashcard 14: Identify the phase shift of $y = 5 \text{cos}(x + \frac{\text{π}}{2})$.

Answer: Phase shift = $-\frac{\text{π}}{2}$. Phase shift = $-\frac{C}{B}$ for the form $\cos(x+C)$.

Flashcard 15: What is the formula for converting degrees to radians?

Answer: Radians = Degrees $\times \frac{\pi}{180}$. Multiply degrees by $\frac{\pi}{180}$ to convert to radians.

Flashcard 16: State the phase shift for $y = \text{cos}(x + \text{π})$.

Answer: Phase shift = $-\text{π}$. For $\cos(x+\pi)$, phase shift = $-\pi$.

Flashcard 17: Convert $60^\text{o}$ to radians.

Answer: $\frac{\text{π}}{3}$. $60° \times \frac{\pi}{180} = \frac{\pi}{3}$ radians.

Flashcard 18: Find the amplitude of $y = -4 \text{cos}(3x)$.

Answer: Amplitude = 4. Amplitude equals $|A|$ regardless of sign.

Flashcard 19: Determine the period of $y = 4 \cos(2x)$.

Answer: Period = $π$. Period = $\frac{2\pi}{|B|}$ where B=2.

Flashcard 20: Identify the vertical shift in $y = 2 \text{sin}(x) + 6$.

Answer: Vertical shift = 6. D represents the upward shift from the x-axis.

Flashcard 21: Convert $90^\text{o}$ to radians.

Answer: $\frac{\text{π}}{2}$. $90° \times \frac{\pi}{180} = \frac{\pi}{2}$ radians.

Flashcard 22: Calculate the period of $y = 2 \text{cos}(0.5x) + 1$.

Answer: Period = $4\text{π}$. Period = $\frac{2\pi}{|B|}$ where B=0.5.

Flashcard 23: Convert $45^\text{o}$ to radians.

Answer: $\frac{\text{π}}{4}$. $45° \times \frac{\pi}{180} = \frac{\pi}{4}$ radians.

Flashcard 24: What is the frequency of $y = \sin(3x)$?

Answer: Frequency = $\frac{3}{2\pi}$. Frequency = $\frac{B}{2\pi}$ where B=3.

Flashcard 25: Which parameter determines the vertical shift in $y = A \text{sin}(B(x - C)) + D$?

Answer: Vertical shift = $D$. D shifts the function up or down from the x-axis.

Flashcard 26: Find the amplitude of $y = -2 \text{cos}(x)$.

Answer: Amplitude = 2. Amplitude is absolute value of coefficient A.

Flashcard 27: What is the general form of a sinusoidal function?

Answer: $y = A \times \sin(B(x - C)) + D$. Standard form where A=amplitude, B affects period, C=phase shift, D=vertical shift.

Flashcard 28: Identify the amplitude of $y = 3 \text{cos}(2x - \frac{\text{π}}{4}) + 1$.

Answer: Amplitude = 3. Amplitude is the absolute value of the coefficient A.

Flashcard 29: Identify the midline for $y = 5 \text{sin}(x) - 3$.

Answer: Midline = $y = -3$. Midline is y equals the vertical shift value.

Flashcard 30: What is the effect of parameter $C$ in $y = A \sin(B(x - C)) + D$?

Answer: $C$ affects the phase shift. $C$ determines horizontal shift left or right.

Flashcard 31: What is the effect of parameter $D$ in $y = A \text{sin}(B(x - C)) + D$?

Answer: $D$ affects the vertical shift. D moves the entire graph up or down vertically.

Flashcard 32: What does the amplitude represent in a sinusoidal function?

Answer: Amplitude is the peak vertical distance from the midline. Maximum deviation from the center line of oscillation.

Flashcard 33: What is the effect of parameter $B$ in $y = A \text{sin}(B(x - C)) + D$?

Answer: $B$ affects the period. B determines how many cycles occur in $2\pi$ units.

Flashcard 34: Identify the midline for $y = -3 \sin(2x) + 5$.

Answer: Midline = $y = 5$. Midline equals the vertical shift $D=5$.

Flashcard 35: Determine the vertical shift of $y = \text{sin}(x) - 4$.

Answer: Vertical shift = $-4$. D value directly gives the vertical displacement.

Flashcard 36: Which parameter affects the amplitude in $y = A \text{sin}(B(x - C)) + D$?

Answer: Amplitude = $|A|$. A controls the vertical stretch and amplitude.

Flashcard 37: Find the amplitude of $y = 7 \text{sin}(x)$.

Answer: Amplitude = 7. Coefficient A directly determines amplitude magnitude.

Flashcard 38: Identify the midline for $y = -3 \text{sin}(2x) + 5$.

Answer: Midline = $y = 5$. Midline equals the vertical shift D=5.

Flashcard 39: State the midline of $y = \text{cos}(x) + 2$.

Answer: Midline = $y = 2$. Midline is the horizontal line y=D.

Flashcard 40: What is the effect of parameter $C$ in $y = A \text{sin}(B(x - C)) + D$?

Answer: $C$ affects the phase shift. C determines horizontal shift left or right.