12. Trigonometric Functions

Given the right triangle below, evaluate $\cos\theta$.

Given the right triangle below, evaluate $\tan\theta$.

If $\tan\theta=\frac{12}{5}$, find the values of the five other trigonometric functions. Rationalize the denominators if necessary.

If $\sin\theta=\frac{\sqrt{17}}{17}$, find the values of the five other trigonometric functions. Rationalize the denominators if necessary.

What is a positive value of A in the interval $\left[0\degree,90\degree\right)$ that will make the following statement true? Express the answer in four decimal places.

$\sin A=0.9235$

What is the positive value of P in the interval $\left[0\degree,90\degree\right)$ that will make the following statement true? Express the answer in four decimal places.

$\cot P=5.2371$

What is the positive value of $D$ in the interval $\left[0,\frac{\pi}{2}\right)$ that will make the following statement true? Express the answer in four decimal places.

$\sec D=3.2842$

Given the triangle below, determine the missing side(s) without using the Pythagorean theorem (make sure your answer is fully simplified).

Without using a calculator, determine all values of P in the interval $\left[0\degree,90\degree\right)$ with the following trigonometric function value.

$\csc P=\sqrt2$

Given the triangle below, determine the missing side(s) without using the Pythagorean theorem (make sure your answer is fully simplified).

Without using a calculator, determine all values of A in the interval $\left[0,\frac{\pi}{2}\right)$ with the following trigonometric function value.

$\cos A=\frac{\sqrt3}{2}$