91Ó°ÊÓ

Sketch an angle \(\theta\) in standard position such that \(\theta\) has the least posi. tive measure, and the given point is on the terminal side of \(\theta .\) Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. $$(-3,4)$$

Sketch an angle \(\theta\) in standard position such that \(\theta\) has the least posi. tive measure, and the given point is on the terminal side of \(\theta .\) Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. $$(7,-24)$$

Suppose ABC is a right triangle with sides of lengths \(a, b,\) and \(c\) and right angle at \(C\). (See Figure 29.) Find the unknown side length using the Pythagorean theorem (Section 1.5 ), and then find the values of the six trigonometric functions for angle \(B\). Rationalize denominators when applicable. $$a=5, b=12$$

Solve each right triangle. In each case, \(C=90^{\circ} .\) If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. $$b=32 \mathrm{ft}, c=51 \mathrm{ft}$$

Suppose that the point \((x, y)\) is in the indicated quadrant. Decide whether the given ratio is positive or negative. Recall that \(r=\sqrt{x^{2}+y^{2}}\). Hint: Draw. ing a sketch may help. $$IV, \frac{x}{y}$$

What is the measure of an angle that is its own supplement?

Find the measure of the smaller angle formed by the hands of a clock at the following times. $$6: 10$$

Suppose that the point \((x, y)\) is in the indicated quadrant. Decide whether the given ratio is positive or negative. Recall that \(r=\sqrt{x^{2}+y^{2}}\). Hint: Draw. ing a sketch may help. $$I, \frac{x}{y}$$

Solve each problem involving triangles. From a window \(30.0 \mathrm{ft}\) above the street, the angle of elevation to the top of the building across the street is \(50.0^{\circ}\) and the angle of depression to the base of this building is \(20.0^{\circ} .\) Find the height of the building across the street. (IMAGES CANNOT COPY)

Suppose that the angle of elevation of the sun is \(23.4^{\circ}\) Find the length of the shadow cast by Dot Peterson, who is \(5.75 \mathrm{ft}\) tall.