2. Trigonometric Functions on Right Triangles

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. cot[n • 180°]

In Exercises 1–8, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ. (-4, 3)

Solve each problem. See Examples 1 and 2. Distance between Two Ships A ship leaves its home port and sails on a bearing of S 61°50'. Another ship leaves the same port at the same time and sails on a bearing of N 28°10'E. If the first ship sails at 24.0 mph and the second sails at 28.0 mph, find the distance between the two ships after 4 hr.

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2.

―15°

In Exercises 61–62, use the figures shown to find the bearing from O to A.

In kite KLMN, if angle K is $49°$ and angle L is $99°$, what is the measure of angle LMN?

In a right triangle, if one leg measures $4$ ft and the hypotenuse measures $8$ ft, what is the length of the other leg $r$?

In a right triangle, one of the acute angles measures $60°$. What is the measure of the other acute angle?

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/y

Triangle QRS is a right triangle with one angle measuring $90°$ and another angle measuring $38°$. What is the measure of the third angle in degrees?

Given that the measure of arc ED is $68°$, what is the measure of angle EFD if angle EFD is an inscribed angle that intercepts arc ED?

Given a right triangle where angle $C$ is the right angle, and the measures of angles $A$ and $B$ are approximately $44.8°$ and $45.2°$ respectively, what is the approximate difference between the measures of angle $C$ and angle $A$?

In right triangle xyz, if angle $y$ is a right angle and the side opposite angle $x$ has length $5$, the side adjacent to angle $x$ has length $12$, and the hypotenuse has length $13$, what is $sinx$?

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1.

sin θ , given that csc θ = 1.25