2. Trigonometric Functions on Right Triangles

Given a right triangle where angle $a$ has an opposite side of length $3$, an adjacent side of length $4$, and a hypotenuse of length $5$, use the triangle to evaluate each function: $\sin \left(a\right)$, $\tan \left(a\right)$, and $\sec \left(a\right)$.

Which of the following statements is true about the tangent function $\tan$ in a right triangle?

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.

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

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

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.

$\sec D=3.2842$