5. Trigonometric Functions

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.

Given the right triangle below, use the sine function to write a trigonometric expression for the missing angle $\theta$.

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

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

$\(\cot\) P=5.2371$.

Given the right triangle below, use the cosine function to write a trigonometric expression for the missing angle $\varphi$.

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