12. Trigonometric Functions

Identify the quadrant that the given angle is located in.

$\frac{7\pi}{4}$ radians

Identify the quadrant that the given angle is located in.

$\frac{\pi}{7}$ radians

Identify the quadrant that the given angle is located in.

$\frac{2\pi}{3}$ radians

Identify the quadrant that the given angle is located in.

$\frac{6\pi}{5}$ radians

Test whether the point is on the unit circle by plugging it into the equation, $x^2+y^2=1$.

$\left(\frac{-\sqrt2}{2},\frac{-\sqrt2}{2}\right)$

Find the sine, cosine, and tangent of each angle using the unit circle.

$\theta=-1.18$ rad, $\left(\frac{5}{13},-\frac{12}{13}\right)$

Find the sine, cosine, and tangent of each angle using the unit circle.

$\theta=225\degree,\left(-\frac{\sqrt2}{2},-\frac{\sqrt2}{2}\right)$

Identify the reference angle of each given angle.

120°

Identify the reference angle of each given angle.

$\frac{7\pi}{4}$ rad

Identify the reference angle of each given angle.

210°

Identify what angle, $\theta$ , satisfies the following conditions.

$\sin\theta=\frac12$; $\tan\theta$ < $0$

Identify what angle, $\theta$ , satisfies the following conditions.

$\cos\theta=\frac{\sqrt3}{2}$; $\sin\theta$ < $0$

Identify what angle, $\theta$ , satisfies the following conditions.

$\tan\theta=-1$; $\cos\theta$ > $0$

For each expression, identify which coterminal angle to use & determine the exact value of the expression.

$\sin\frac{7\pi}{3}$

For each expression, identify which coterminal angle to use & determine the exact value of the expression.

$\tan765\degree$