AP Precalculus Flashcards: Sine And Cosine Function Values

What this deck covers

This deck focuses on Sine And Cosine Function Values, 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: Which is greater: $\text{sin}(\frac{\text{π}}{4})$ or $\text{cos}(\frac{\text{π}}{4})$?

Answer: Equal. Both equal $\frac{\sqrt{2}}{2}$ at the 45° angle.

Flashcard 2: What is the value of $\text{cos}(\text{π})$?

Answer: -1. At $\pi$, we're at the leftmost point where x-coordinate is -1.

Flashcard 3: What is the value of $\text{sin}(\frac{3\text{π}}{2})$?

Answer: -1. At $\frac{3\pi}{2}$, we're at the bottom of the unit circle.

Flashcard 4: Evaluate $\text{cos}(270^\text{o})$.

Answer:

1. 270° is equivalent to $\frac{3\pi}{2}$ radians.

Flashcard 5: What is the phase shift of $y = \text{cos}(x + \frac{\text{π}}{3})$?

Answer: $\frac{\text{π}}{3}$ to the left. Horizontal shift is $-\frac{C}{B}$ where $C=-\frac{\pi}{3}$ and $B=1$.

Flashcard 6: Find $\sin(-\pi)$ using symmetry.

Answer:

1. Sine is an odd function: $\sin(-x) = -\sin(x)$.

Flashcard 7: What is the value of $\text{sin}(\text{π})$?

Answer:

1. At $\pi$, we're at the leftmost point where y-coordinate is zero.

Flashcard 8: Evaluate $\text{cos}(90^\text{o})$.

Answer:

1. 90° is equivalent to $\frac{\pi}{2}$ radians.

Flashcard 9: What is the cosine of a 45-degree angle?

Answer: $\frac{\sqrt{2}}{2}$. 45° corresponds to $\frac{\pi}{4}$ radians on the unit circle.

Flashcard 10: Identify the range of $y = \text{cos}(x)$.

Answer: [-1, 1]. Cosine oscillates between its maximum and minimum values.

Flashcard 11: Identify the range of $y = \text{sin}(x)$.

Answer: [-1, 1]. Sine oscillates between its maximum and minimum values.

Flashcard 12: Find $\text{sin}(-\text{π})$ using symmetry.

Answer:

1. Sine is an odd function: $\sin(-x) = -\sin(x)$.

Flashcard 13: Evaluate $\sin\left(\frac{\pi}{3}\right)$.

Answer: $\frac{\sqrt{3}}{2}$. 60° angle corresponds to the longer leg in a 30-60-90 triangle.

Flashcard 14: What is the reciprocal of $\sin(x)$?

Answer: $\csc(x)$. Cosecant is defined as $\frac{1}{\sin(x)}$.

Flashcard 15: What is the amplitude of $y = -2\text{cos}(x)$?

Answer:

1. Amplitude is the absolute value of the coefficient of cosine.

Flashcard 16: What is the value of $\text{cos}(\frac{3\text{π}}{2})$?

Answer:

1. At $\frac{3\pi}{2}$, the x-coordinate is zero.

Flashcard 17: What is the sine of a 45-degree angle?

Answer: $\frac{\sqrt{2}}{2}$. 45° corresponds to $\frac{\pi}{4}$ radians on the unit circle.

Flashcard 18: Evaluate $\sin(\frac{\pi}{3})$.

Answer: $\frac{\sqrt{3}}{2}$. 60° angle corresponds to the longer leg in a 30-60-90 triangle.

Flashcard 19: What is the period of $y = \cos(\frac{x}{2})$?

Answer: $4\pi$. Period equals $\frac{2\pi}{|B|}$ where $B=\frac{1}{2}$.

Flashcard 20: What is the phase shift of $y = \text{sin}(x - \frac{\text{π}}{4})$?

Answer: $\frac{\text{π}}{4}$ to the right. Horizontal shift is $\frac{C}{B}$ where $C=\frac{\pi}{4}$ and $B=1$.

Flashcard 21: What is the period of $y = \text{cos}(\frac{x}{2})$?

Answer: $4\text{π}$. Period equals $\frac{2\pi}{|B|}$ where $B=\frac{1}{2}$.

Flashcard 22: Evaluate $\text{cos}(360^\text{o})$.

Answer:

1. 360° is equivalent to $2\pi$ radians.

Flashcard 23: Evaluate $\text{sin}(270^\text{o})$.

Answer: -1. 270° is equivalent to $\frac{3\pi}{2}$ radians.

Flashcard 24: What is the reciprocal of $\text{cos}(x)$?

Answer: $\text{sec}(x)$. Secant is defined as $\frac{1}{\cos(x)}$.

Flashcard 25: Evaluate $\text{cos}(180^\text{o})$.

Answer: -1. 180° is equivalent to $\pi$ radians.

Flashcard 26: Evaluate $\text{sin}(\frac{\text{π}}{6})$.

Answer: $\frac{1}{2}$. 30° angle gives the smallest positive sine value in special triangles.

Flashcard 27: What is the value of $\text{sin}(2\text{π})$?

Answer:

1. After one complete revolution, we return to the starting y-coordinate.

Flashcard 28: Evaluate $\text{sin}(360^\text{o})$.

Answer:

1. 360° is equivalent to $2\pi$ radians.

Flashcard 29: What is the value of $\text{sin}(0)$?

Answer:

1. At the origin, sine is the y-coordinate on the unit circle.

Flashcard 30: What is the frequency of $y = \cos(5x)$?

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

Flashcard 31: What is the period of $y = \text{sin}(2x)$?

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

Flashcard 32: What is the value of $\text{cos}(0)$?

Answer:

1. At the origin, cosine is the x-coordinate on the unit circle.

Flashcard 33: Evaluate $\text{cos}(\frac{\text{π}}{3})$.

Answer: $\frac{1}{2}$. 60° angle gives the smallest positive cosine value in special triangles.

Flashcard 34: What is the value of $\text{cos}(\frac{\text{π}}{2})$?

Answer:

1. At $\frac{\pi}{2}$, the x-coordinate is zero.

Flashcard 35: Evaluate $\cos\left(\frac{\pi}{6}\right)$.

Answer: $\frac{\sqrt{3}}{2}$. 30° angle corresponds to the longer leg in a 30-60-90 triangle.

Flashcard 36: What is the value of $\text{cos}(2\text{π})$?

Answer:

1. After one complete revolution, we return to the starting x-coordinate.

Flashcard 37: What is the amplitude of $y = 3\text{sin}(x)$?

Answer:

1. Amplitude is the absolute value of the coefficient of sine.

Flashcard 38: Find $\text{cos}(-\text{π})$ using symmetry.

Answer: -1. Cosine is an even function: $\cos(-x) = \cos(x)$.

Flashcard 39: What is the period of $y = \sin(2x)$?

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

Flashcard 40: Evaluate $\text{sin}(90^\text{o})$.

Answer:

1. 90° is equivalent to $\frac{\pi}{2}$ radians.

Flashcard 41: What is the value of $\text{cos}(\text{π} - x)$?

Answer: $-\text{cos}(x)$. Uses the cosine supplementary angle identity.

Flashcard 42: What is the value of $\text{sin}(\frac{\text{π}}{2})$?

Answer:

1. At $\frac{\pi}{2}$, we reach the top of the unit circle.

Flashcard 43: Evaluate $\text{sin}(180^\text{o})$.

Answer:

1. 180° is equivalent to $\pi$ radians.