2. Trigonometric Functions on Right Triangles

In a right triangle ABC with right angle at $C$, if $\mathrm{AD}$ is the altitude from vertex $A$ to the hypotenuse $\mathrm{BC}$, which of the following is true about the relationship between the segments $\mathrm{BD}$, $\mathrm{DC}$, and $\mathrm{AD}$?

Concept Check Suppose that 90° < θ < 180° .   Find the sign of each function value. cos ( ―θ)

Triangle $ABC$ is rotated $100°$ counterclockwise about point $P$ to create triangle $\mathrm{A\text{'}}\mathrm{B\text{'}}\mathrm{C\text{'}}$. What is the measure of angle $\angle \mathrm{C\text{'}}\mathrm{A\text{'}}\mathrm{B\text{'}}$?

An equation of the terminal side of an angle θ in standard position is given with a restriction on x. Sketch the least positive such angle θ , and find the values of the six trigonometric functions of θ . 12x + 5y = 0 , x ≥ 0 .

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods. (-3, -3)

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.) IV , x/r

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

csc θ = ―3 , and cos θ > 0

Triangle xyz is reflected across the y-axis, and point $x$ has coordinates $(4,-5)$. What are the coordinates of $x\text{'}$ after the reflection?

In Exercises 9–16, evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. tan 𝜋

Given a right triangle ABC with right angle at C, which of the following is the correct trigonometric ratio for $\angle A$?

Concept Check Find a solution for each equation. tan (3θ ― 4°) = 1 / [cot(5θ ― 8°)]

In circle D, if $\angle EDH$ is congruent to $\angle EDG$, what is the measure of $\angle EDH$? Choose the correct answer below.

Which trigonometric functions have a domain of $[-1,1]$?

In Exercises 63–68, find the exact value of each expression. Do not use a calculator. 1 + sin² 40° + sin² 50°

Given a right triangle where $m\angle ABC$ is one of the angles, which of the following could be the measure of $m\angle ABC$?