12. Trigonometric Functions

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

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

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

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 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$

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=\(\frac{\sqrt3}{2}\)$

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

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$

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

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=\(\sqrt\)2$

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