91Ó°ÊÓ

Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. $$512^{\circ}$$

Decide whether each statement is possible or impossible for some angle \(\theta\). $$\csc \theta=100$$

Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. $$-180^{\circ}$$

Find a value of \(\theta\) in the interval \(\left[0^{\circ}, 90^{\circ}\right]\) that satisfies each statement. Write each answer in decimal degrees to six decimal places as needed. See Example \(8 .\) $$\csc \theta=4.7216543$$

Find the five remaining trigonometric finction values for each angle. \(\tan \theta=\sqrt{3},\) and \(\theta\) is in quadrant III.

A turntable in a shop makes 45 revolutions per min. How many revolutions does it make per second?

A windmill makes 90 revolutions per min. How many revolutions does it make per second?

An airplane propeller rotates 1000 times per min. Find the number of degrees that a point on the edge of the propeller will rotate in 1 sec.

A pulley rotates through \(75^{\circ}\) in 1 min. How many rotations does the pulley make in an hour?

As a consequence of Earth's rotation, celestial objects such as the moon and the stars appear to move across the sky, rising in the east and setting in the west. As a result, if a telescope on Earth remains stationary while viewing a celestial object, the object will slowly move outside the viewing field of the telescope. For this reason, a motor is often attached to telescopes so that the telescope rotates at the same rate as Earth. Determine how long it should take the motor to turn the telescope through an angle of 1 min in a direction perpendicular to Earth's axis.