91Ó°ÊÓ

Change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$-3.642 \mathrm{rad}$$

Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$0.329 \mathrm{rad}$$

Find the values of the indicated functions. In Exercises \(17-20,\) give answers in exact form. In Exercises \(21-24,\) the values are approximate. Given \(\sin \theta=0.750,\) find \(\cot \theta\) and \(\csc \theta\).

Solve the given problems. Sketch an appropriate figure, unless the figure is given. The angle of inclination of a road is often expressed as percent grade, which is the vertical rise divided by the horizontal run (expressed as a percent). See Fig. 4.57. A 6.0\% grade corresponds to a road that rises \(6.0 \mathrm{ft}\) for every \(100 \mathrm{ft}\) along the horizontal. Find the angle of inclination that corresponds to a 6.0\% grade.

Solve the given problems. Sketch an appropriate figure, unless the figure is given. A circular patio table of diameter \(1.20 \mathrm{m}\) has a regular octagon design inscribed within the outer edge (all eight vertices touch the circle). What is the perimeter of the octagon?

Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$2.089 \mathrm{rad}$$

Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$-4.110 \mathrm{rad}$$

Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest \(0.01^{\circ}\) $$6.705 rad$$

find the values of the indicated functions. In Exer. cises \(17-20,\) give answers in exact form. In Exercises \(21-24,\) the val. ues are approximate. Given \(\csc \theta=1.20,\) find \(\sec \theta\) and \(\cos \theta.\)

Solve the given problems. Sketch an appropriate figure, unless the figure is given. From a space probe circling Io, one of Jupiter's moons, at an altitude of \(552 \mathrm{km},\) it was observed that the angle of depression of the horizon was \(39.7^{\circ} .\) What is the radius of Io?