3. Unit Circle

Find each exact function value.

tan π/3

Find the angular speed ω for each of the following.

a gear revolving 300 times per min

Find the angular speed ω for each of the following.

a wind turbine with blades turning at a rate of 15 revolutions per minute

Find a calculator approximation to four decimal places for each circular function value. See Example 3. tan 4.0203

Find each exact function value.

sin ( ―5π/6)

Find the linear speed v for each of the following.

the tip of the minute hand of a clock, if the hand is 7 cm long

Find a calculator approximation to four decimal places for each circular function value. See Example 3. csc (―9.4946)

Find each exact function value.

csc ( ―11π/6)

Find the linear speed v for each of the following.

a point on the edge of a flywheel of radius 2 m, rotating 42 times per min

Find a calculator approximation to four decimal places for each circular function value. See Example 3.

sec 2.8440

Without using a calculator, determine which of the two values is greater.

tan 1 or tan 2

Find the linear speed v for each of the following.

the tip of a propeller 3 m long, rotating 500 times per min (Hint: r = 1.5 m)

Find a calculator approximation to four decimal places for each circular function value. See Example 3.

cot 6.0301

Without using a calculator, determine which of the two values is greater.

cos 2 or sin 2

Find the linear speed v for each of the following.

a point on the equator moving due to Earth's rotation, if the radius is 3960 mi