Sine and Cosine Function Values - AP Precalculus
Card 1 of 30
Find $\text{cos}(-\text{π})$ using symmetry.
Find $\text{cos}(-\text{π})$ using symmetry.
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-1. Cosine is an even function: $\cos(-x) = \cos(x)$.
-1. Cosine is an even function: $\cos(-x) = \cos(x)$.
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Evaluate $\text{cos}(\frac{\text{π}}{3})$.
Evaluate $\text{cos}(\frac{\text{π}}{3})$.
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$\frac{1}{2}$. 60° angle gives the smallest positive cosine value in special triangles.
$\frac{1}{2}$. 60° angle gives the smallest positive cosine value in special triangles.
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Evaluate $\text{sin}(270^\text{o})$.
Evaluate $\text{sin}(270^\text{o})$.
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-1. 270° is equivalent to $\frac{3\pi}{2}$ radians.
-1. 270° is equivalent to $\frac{3\pi}{2}$ radians.
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Evaluate $\text{cos}(270^\text{o})$.
Evaluate $\text{cos}(270^\text{o})$.
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- 270° is equivalent to $\frac{3\pi}{2}$ radians.
- 270° is equivalent to $\frac{3\pi}{2}$ radians.
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Evaluate $\text{sin}(360^\text{o})$.
Evaluate $\text{sin}(360^\text{o})$.
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- 360° is equivalent to $2\pi$ radians.
- 360° is equivalent to $2\pi$ radians.
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Evaluate $\text{cos}(360^\text{o})$.
Evaluate $\text{cos}(360^\text{o})$.
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- 360° is equivalent to $2\pi$ radians.
- 360° is equivalent to $2\pi$ radians.
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Find $\text{sin}(-\text{π})$ using symmetry.
Find $\text{sin}(-\text{π})$ using symmetry.
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- Sine is an odd function: $\sin(-x) = -\sin(x)$.
- Sine is an odd function: $\sin(-x) = -\sin(x)$.
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Find $\text{cos}(-\text{π})$ using symmetry.
Find $\text{cos}(-\text{π})$ using symmetry.
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-1. Cosine is an even function: $\cos(-x) = \cos(x)$.
-1. Cosine is an even function: $\cos(-x) = \cos(x)$.
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What is the reciprocal of $\text{cos}(x)$?
What is the reciprocal of $\text{cos}(x)$?
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$\text{sec}(x)$. Secant is defined as $\frac{1}{\cos(x)}$.
$\text{sec}(x)$. Secant is defined as $\frac{1}{\cos(x)}$.
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What is the frequency of $y = \cos(5x)$?
What is the frequency of $y = \cos(5x)$?
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$\frac{5}{2\pi}$. Frequency is $\frac{|B|}{2\pi}$ where $B=5$.
$\frac{5}{2\pi}$. Frequency is $\frac{|B|}{2\pi}$ where $B=5$.
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What is the value of $\text{cos}(\text{π} - x)$?
What is the value of $\text{cos}(\text{π} - x)$?
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$ -\text{cos}(x) $. Uses the cosine supplementary angle identity.
$ -\text{cos}(x) $. Uses the cosine supplementary angle identity.
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What is the cosine of a 45-degree angle?
What is the cosine of a 45-degree angle?
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$\frac{\sqrt{2}}{2}$. 45° corresponds to $\frac{\pi}{4}$ radians on the unit circle.
$\frac{\sqrt{2}}{2}$. 45° corresponds to $\frac{\pi}{4}$ radians on the unit circle.
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What is the reciprocal of $\sin(x)$?
What is the reciprocal of $\sin(x)$?
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$\csc(x)$. Cosecant is defined as $\frac{1}{\sin(x)}$.
$\csc(x)$. Cosecant is defined as $\frac{1}{\sin(x)}$.
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What is the value of $\text{cos}(2\text{π})$?
What is the value of $\text{cos}(2\text{π})$?
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- After one complete revolution, we return to the starting x-coordinate.
- After one complete revolution, we return to the starting x-coordinate.
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Evaluate $\text{cos}(360^\text{o})$.
Evaluate $\text{cos}(360^\text{o})$.
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- 360° is equivalent to $2\pi$ radians.
- 360° is equivalent to $2\pi$ radians.
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What is the value of $\text{sin}(2\text{π})$?
What is the value of $\text{sin}(2\text{π})$?
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- After one complete revolution, we return to the starting y-coordinate.
- After one complete revolution, we return to the starting y-coordinate.
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Identify the range of $y = \text{sin}(x)$.
Identify the range of $y = \text{sin}(x)$.
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[-1, 1]. Sine oscillates between its maximum and minimum values.
[-1, 1]. Sine oscillates between its maximum and minimum values.
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Evaluate $\text{sin}(\frac{\text{π}}{6})$.
Evaluate $\text{sin}(\frac{\text{π}}{6})$.
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$\frac{1}{2}$. 30° angle gives the smallest positive sine value in special triangles.
$\frac{1}{2}$. 30° angle gives the smallest positive sine value in special triangles.
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Evaluate $\text{cos}(\frac{\text{π}}{3})$.
Evaluate $\text{cos}(\frac{\text{π}}{3})$.
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$\frac{1}{2}$. 60° angle gives the smallest positive cosine value in special triangles.
$\frac{1}{2}$. 60° angle gives the smallest positive cosine value in special triangles.
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What is the amplitude of $y = 3\text{sin}(x)$?
What is the amplitude of $y = 3\text{sin}(x)$?
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- Amplitude is the absolute value of the coefficient of sine.
- Amplitude is the absolute value of the coefficient of sine.
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What is the amplitude of $y = -2\text{cos}(x)$?
What is the amplitude of $y = -2\text{cos}(x)$?
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- Amplitude is the absolute value of the coefficient of cosine.
- Amplitude is the absolute value of the coefficient of cosine.
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What is the phase shift of $y = \text{sin}(x - \frac{\text{π}}{4})$?
What is the phase shift of $y = \text{sin}(x - \frac{\text{π}}{4})$?
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$\frac{\text{π}}{4}$ to the right. Horizontal shift is $\frac{C}{B}$ where $C=\frac{\pi}{4}$ and $B=1$.
$\frac{\text{π}}{4}$ to the right. Horizontal shift is $\frac{C}{B}$ where $C=\frac{\pi}{4}$ and $B=1$.
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What is the phase shift of $y = \text{cos}(x + \frac{\text{π}}{3})$?
What is the phase shift of $y = \text{cos}(x + \frac{\text{π}}{3})$?
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$\frac{\text{π}}{3}$ to the left. Horizontal shift is $-\frac{C}{B}$ where $C=-\frac{\pi}{3}$ and $B=1$.
$\frac{\text{π}}{3}$ to the left. Horizontal shift is $-\frac{C}{B}$ where $C=-\frac{\pi}{3}$ and $B=1$.
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What is the period of $y = \cos(\frac{x}{2})$?
What is the period of $y = \cos(\frac{x}{2})$?
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$4\pi$. Period equals $\frac{2\pi}{|B|}$ where $B=\frac{1}{2}$.
$4\pi$. Period equals $\frac{2\pi}{|B|}$ where $B=\frac{1}{2}$.
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What is the period of $y = \sin(2x)$?
What is the period of $y = \sin(2x)$?
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$\pi$. Period equals $\frac{2\pi}{|B|}$ where $B=2$.
$\pi$. Period equals $\frac{2\pi}{|B|}$ where $B=2$.
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What is the reciprocal of $\sin(x)$?
What is the reciprocal of $\sin(x)$?
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$\csc(x)$. Cosecant is defined as $\frac{1}{\sin(x)}$.
$\csc(x)$. Cosecant is defined as $\frac{1}{\sin(x)}$.
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What is the amplitude of $y = 3\text{sin}(x)$?
What is the amplitude of $y = 3\text{sin}(x)$?
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- Amplitude is the absolute value of the coefficient of sine.
- Amplitude is the absolute value of the coefficient of sine.
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What is the value of $\text{cos}(\text{π})$?
What is the value of $\text{cos}(\text{π})$?
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-1. At $\pi$, we're at the leftmost point where x-coordinate is -1.
-1. At $\pi$, we're at the leftmost point where x-coordinate is -1.
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What is the value of $\text{sin}(0)$?
What is the value of $\text{sin}(0)$?
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- At the origin, sine is the y-coordinate on the unit circle.
- At the origin, sine is the y-coordinate on the unit circle.
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What is the value of $\text{cos}(0)$?
What is the value of $\text{cos}(0)$?
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- At the origin, cosine is the x-coordinate on the unit circle.
- At the origin, cosine is the x-coordinate on the unit circle.
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