12. Trigonometric Functions

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

$\(\tan\)765\(\degree\)$

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

$\(\cos\[\left\)(-\(\frac{10\pi}{4}\]\right\))$

Evaluate each expression.

$\(\cot\[\left\)(\(\frac{11\pi}{6}\]\right\))$

Identify the quadrant that the given angle is located in.

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

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 quadrant that the given angle is located in.

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

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

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

Evaluate each expression.

$\(\csc\)225\(\degree\)$

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

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

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

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

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

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

Identify the reference angle of each given angle.

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

Identify the quadrant that the given angle is located in.

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

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

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

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

$\(\sin\)\(\theta\)=\(\frac\)12$; $\(\tan\)\(\theta\)$ < $0$