2. Trigonometric Functions on Right Triangles

Which of the following statements best describes the relationship between the acute angles in a right triangle according to the linear pair perpendicular theorem?

In right triangle $MLO$, angle $MLO$ measures $112°$. What is the measure of angle $MLP$?

In the figure above, points $P$ and $Q$ lie on a circle with center $O$. If triangle $OPQ$ is a right triangle with right angle at $P$, and $OP=5$, $OQ=13$, what is the value of $PQ$ (denoted as $s$)?

Given a right triangle $△abc$ where angle $a$ is one of the acute angles, if $\sin \left(a\right)=\frac{3}{5}$, $\cos \left(a\right)=\frac{4}{5}$, and $\tan \left(a\right)=\frac{3}{4}$, which of the following triangles is similar to $△abc$?

If $\theta$ is an angle such that $\sin \left(\theta \right)=0.3030$, what is the approximate value of $\csc \left(\theta \right)$?

Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3. cos θ > 0 , sec θ > 0

Given a right triangle where angle $A$ measures $39°$ and side $\mathrm{BC}$ is the hypotenuse, what is the measure of arc $\mathrm{BC}$ in degrees?

In a right triangle, which pair of angles shares ray $AF$ as a common side? Choose the correct pair from the options below.

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

Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. sec θ = 1.2637891

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

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 .

If n is an integer, n • 180° represents an integer multiple of 180°, (2n + 1) • 90° represents an odd integer multiple of 90° , and so on. Determine whether each expression is equal to 0, 1, or ―1, or is undefined. cos[n • 360°]

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.

sin θ = √2/6 , and cos θ < 0

In square $ABCD$, what is the measure of angle $\angle BAC$?