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 $\text{sin}(0)$?

Answer:

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

Flashcard 3: 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 4: 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 5: Evaluate $\text{cos}(270^\text{o})$.

Answer:

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

Flashcard 6: Find $\text{cos}(-\text{π})$ using symmetry.

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

Flashcard 7: 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 8: Find $\sin(-\pi)$ using symmetry.

Answer:

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

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

Answer:

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

Flashcard 12: 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 13: Identify the range of $y = \text{cos}(x)$.

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

Flashcard 14: Identify the range of $y = \text{sin}(x)$.

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

Flashcard 15: Find $\text{sin}(-\text{π})$ using symmetry.

Answer:

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

Flashcard 16: Evaluate $\text{sin}(\frac{\text{π}}{6})$.

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

Flashcard 17: 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 18: What is the reciprocal of $\sin(x)$?

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

Flashcard 19: What is the amplitude of $y = -2\text{cos}(x)$?

Answer:

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

Flashcard 20: 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 21: What is the value of $\text{cos}(\frac{\text{π}}{2})$?

Answer:

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

Flashcard 22: What is the value of $\text{cos}(\text{π} - x)$?

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

Flashcard 23: 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 24: Evaluate $\sin(\frac{\pi}{3})$.

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

Flashcard 25: 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 26: What is the value of $\text{sin}(2\text{π})$?

Answer:

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

Flashcard 27: 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 28: 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 29: Evaluate $\text{cos}(360^\text{o})$.

Answer:

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

Flashcard 30: Evaluate $\text{sin}(270^\text{o})$.

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

Flashcard 31: 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 32: What is the reciprocal of $\text{cos}(x)$?

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

Flashcard 33: Evaluate $\text{cos}(180^\text{o})$.

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

Flashcard 34: 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 35: Evaluate $\text{sin}(\frac{\text{π}}{6})$.

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

Flashcard 36: What is the reciprocal of $\text{cos}(x)$?

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

Flashcard 37: Evaluate $\text{cos}(360^\text{o})$.

Answer:

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

Flashcard 38: What is the value of $\text{sin}(2\text{π})$?

Answer:

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

Flashcard 39: What is the value of $\text{cos}(0)$?

Answer:

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

Flashcard 40: Evaluate $\text{sin}(360^\text{o})$.

Answer:

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

Flashcard 41: 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 42: Evaluate $\text{cos}(180^\text{o})$.

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

Flashcard 43: What is the value of $\text{sin}(0)$?

Answer:

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

Flashcard 44: What is the frequency of $y = \cos(5x)$?

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

Flashcard 45: What is the period of $y = \text{sin}(2x)$?

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

Flashcard 46: Evaluate $\text{sin}(180^\text{o})$.

Answer:

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

Flashcard 47: What is the amplitude of $y = 3\text{sin}(x)$?

Answer:

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

Flashcard 48: What is the value of $\text{cos}(0)$?

Answer:

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

Flashcard 49: Evaluate $\text{cos}(270^\text{o})$.

Answer:

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

Flashcard 50: Evaluate $\text{sin}(270^\text{o})$.

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

Flashcard 51: Evaluate $\text{cos}(\frac{\text{π}}{3})$.

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

Flashcard 52: Evaluate $\text{cos}(\frac{\text{π}}{3})$.

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

Flashcard 53: What is the value of $\text{cos}(\frac{\text{π}}{2})$?

Answer:

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

Flashcard 54: What is the reciprocal of $\sin(x)$?

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

Flashcard 55: 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 56: What is the amplitude of $y = -2\text{cos}(x)$?

Answer:

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

Flashcard 57: 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 58: What is the sine of a 45-degree angle?

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

Flashcard 59: What is the value of $\text{cos}(2\text{π})$?

Answer:

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

Flashcard 60: What is the amplitude of $y = 3\text{sin}(x)$?

Answer:

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

Flashcard 61: Evaluate $\text{sin}(90^\text{o})$.

Answer:

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

Flashcard 62: Evaluate $\text{sin}(360^\text{o})$.

Answer:

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

Flashcard 63: 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 64: What is the value of $\text{cos}(2\text{π})$?

Answer:

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

Flashcard 65: Find $\text{cos}(-\text{π})$ using symmetry.

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

Flashcard 66: 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 67: What is the period of $y = \sin(2x)$?

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

Flashcard 68: What is the frequency of $y = \cos(5x)$?

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

Flashcard 69: Evaluate $\text{sin}(90^\text{o})$.

Answer:

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

Flashcard 70: What is the value of $\text{cos}(\text{π} - x)$?

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

Flashcard 71: 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 72: Identify the range of $y = \text{sin}(x)$.

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

Flashcard 73: Evaluate $\text{sin}(180^\text{o})$.

Answer:

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

Flashcard 74: 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 75: Identify the range of $y = \text{cos}(x)$.

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

Flashcard 76: Evaluate $\text{cos}(90^\text{o})$.

Answer:

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