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$

CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. Given tan θ = 1/cot θ , two equivalent forms of this identity are cot θ = 1/______ and tan θ . ______ = 1 .

CONCEPT PREVIEW Determine whether each statement is possible or impossible. sin θ = 1/2 , csc θ = 2

CONCEPT PREVIEW Determine whether each statement is possible or impossible. cos θ = 1.5

CONCEPT PREVIEW Determine whether each statement is possible or impossible. sin² θ + cos² θ = 2