Sine, Cosine, and Tangent - AP Precalculus

Cosecant. Cosecant is $\frac{1}{\sin(x)}$.

1. The coefficient of the sine function is the amplitude.

Secant. Secant is $\frac{1}{\cos(x)}$.

1. The coefficient of the sine function is the amplitude.

1. The absolute value of the coefficient is the amplitude.

3 units up. Adding a constant outside the function shifts vertically.

Negative. Cosine is negative in Quadrants II and III.

Negative. Tangent is negative in Quadrants II and IV.

$30^\text{o}$. Reference angle is $210° - 180° = 30°$.

$\frac{\pi}{6}$ to the left. A positive value inside parentheses shifts the graph left.

1. This is a standard angle value on the unit circle.

$\frac{1}{2}$. This is a standard angle value on the unit circle.

$\frac{\pi}{6}$. Reference angle is $\frac{7\pi}{6} - \pi = \frac{\pi}{6}$.

$\frac{\pi}{4}$ to the right. A negative value inside parentheses shifts the graph right.

$x = n\pi$, where $n \text{ is an integer}$. Sine equals zero at integer multiples of $\pi$.

$\pi$. Tangent repeats its values every $\pi$ radians.

$\frac{1}{2}$. This is a standard angle value on the unit circle.

Negative. Cosine is negative in Quadrants II and III.

$60^\text{o}$. Use the formula $\text{degrees} = \text{radians} \times \frac{180°}{\pi}$.

$\frac{4}{5}$. Use $\sin^2 A + \cos^2 A = 1$ to find $\sin A = \sqrt{1 - (\frac{3}{5})^2}$.

1. At $0°$, the point is $(1, 0)$ on the unit circle.

1. The absolute value of the coefficient is the amplitude.

1. At $90°$, the point is $(0, 1)$ on the unit circle.

$2\pi$. Cosine repeats its values every $2\pi$ radians.

$\frac{\pi}{6}$. Reference angle is $\frac{7\pi}{6} - \pi = \frac{\pi}{6}$.

1. Since $\tan(\pi) = \frac{\sin(\pi)}{\cos(\pi)} = \frac{0}{-1}$.

$2\pi$. Cosine repeats its values every $2\pi$ radians.

$2\pi$. Sine repeats its values every $2\pi$ radians.

$60^\circ$. Use the formula $\text{degrees} = \text{radians} \times \frac{180^\circ}{\pi}$