Exam 2 - Pre Calculus

A circle of radius r = 2 is shown below. * Draw an arc with length s = 1/3 * 4pie. * When you are done drawing the arc, an angle 0 will be shown. Find 0. Write your answer in radians in terms of pie. (You need not simplify your answer.)

0 = 1/3 * 2pie radians

Round your answer to the nearest hundredth. If applicable, click on "Undefined." For each expression, make sure you are in the correct calculator mode. csc45 degrees = cot(-180 degrees) = sec(-5pie/8) =

1.41 Undefined -2.61

Answer the following. Round your answer to the nearest hundredth. (a) Convert 160.63 degrees to radian measure. (b) Convert -2.7 radians to degree measure.

2.80 radians -154.70 degrees

A ceiling fan has 15-inch blades (so the radius of the circular fan is 15 inches). Suppose the fan turns at a rate of 67 revolutions per minute. (a) Find the angular speed of the fan in radians per minute. (b) Find the linear speed of the tip of a blade in inches per minute. Do not round any intermediate computations, and round your answer to the nearest whole number.

421 radians per minute 6315 inches per minute

A larger gear has a radius of 43 cm, and a smaller gear has a radius of 29 cm. As the larger gear turns 01 radians, it turns the smaller gear 02 radians. (a) Express the angel 02 as a function f of the angle 01. Your answer should be an expression using the variable 01. Give exact values in your answer (not decimal approximations). 02 = f(01) = (b) If the larger gear makes one half of a revolution, how many radians will the smaller gear turn? Write your answer in radians in terms of pie.

43/29 01 43pie/29 radians

Rationalize the denominator and simplify 8/sqrt(10)

4sqrt(10)/5

A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment, he is located 54 meters from one entrance of the tunnel, at an angle of 56 degrees to the perpendicular. Also according to his equipment, he is 31 meters from the other entrance of the tunnel, at an angle of 13 degrees to the perpendicular. Based on these measurements, find the length of the entire tunnel. Do not round any intermediate computations. Round your answer to the nearest tenth. Note that the figure below is not drawn to scale.

51.8 meters

A kite flying in the air has an 81-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 41 degrees. Find the height of the kite. Round your answer to the nearest tenth.

53.1 ft

Solve the right triangle. Round your answer to the nearest tenth.

B = 43 degrees b = 16.8 c = 24.6

A right triangle has side lengths 8, 15, and 17 as shown below. Use these lengths to find cos L, tan L, and sin L.

cos L = 15/17 tan L = 8/15 sin L = 8/17

On the unit circle, sketch 0 = 2.15pie radians in standard position. Then use the coordinates shown, which are rounded to the hundredths place, to find cos(-2.15pie) and sin(-2.15pie). Write your answer to the hundredths place.

cos(-2.15pie) = 0.89 sin(-2.15pie) = -0.45

A right triangle has side lengths, a, b, and c as shown below. Use these lengths to find sin x, tan x, and cos x.

sin x = a/b tan x = a/c cos x = c/b

A right triangle has side lengths d, e, and f as shown below. Use these lengths to find sin x, tan x, and cos x.

sin x = f/e, tan x = f/d, cos s = d/e

Solve for x in the triangle. Round your answer to the nearest tenth.

x = 12.7

A ramp 23 ft long rises to a platform. The bottom of the platform is 10 ft from the foot of the ramp. Find x, the angle of elevation of the ramp. Round your answer to the nearest tenth of a degree.

x = 64.2 degrees