2. Trigonometric Functions on Right Triangles

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

cos 30°

In Exercises 33–42, let sin t = a, cos t = b, and tan t = c. Write each expression in terms of a, b, and c. 3 cos(-t) - cos t

Given a right triangle where angle $A$ is the right angle, what is the measure of angle $B$ if angle $C$ is $15°$?

In the context of right triangles, which of the following best describes when the $\tan$ function can be applied to relate a line and an arc?

Given a right triangle where the side opposite angle $\theta$ has length $3$, the adjacent side has length $4$, and the hypotenuse has length $5$, what is the equation for the trigonometric function $f\left(x\right)$ that represents $sin$ of angle $\theta$ in terms of these side lengths?

Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) I , r/y

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

tan 𝜋/4 + csc 𝜋/6

Determine whether each statement is possible or impossible. See Example 4. sin θ = 3

The ? side of a triangle is the side next to the reference angle and connected to the right angle.

If $\mathrm{angle}2$ is congruent to $\mathrm{angle}6$ in two right triangles, which of the following statements is true about the ratios of their corresponding sides?

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7. tan θ = ―15/8 , and θ is in quadrant II .

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

In a right triangle, if the length of the adjacent side to angle $\theta$ is $12\mathrm{cm}$ and the length of the hypotenuse is $13\mathrm{cm}$, what is the value of $\cos \left(\theta \right)$?

Given a right triangle with angles measuring $15°$, $29°$, and $136°$, what is the measure of the smallest angle?