1. Suppose you wanted to give a cosine function an inverse by restricting its do

Question

1. Suppose you wanted to give a cosine function an inverse by restricting its domain to [pi, k] for some value of k. What should the value of k be?

A. 3pi
B. pi/2
C. 2pi
D. 3pi/2

2. Cesar is building a shelf at an angle so that it appears to be leaning against the wall. The shelf touches the wall 7 ft. above the floor and the distance along the floor from the wall to the front of the shelf is 1.5 ft. What is the angle the shelf makes with the floor?

A. 77.9 degrees
B. 77.6 degrees
C. 12.1 degrees
D. 12.4 degrees

3. A 15-ft. building casts a shadow of 12 ft. What is the approximate angle of inclination of the sun?

A. 51.3 degrees
B. 53.1 degrees
C. 36.9 degrees
D. 19.2 degrees

Thank you for your help in advance!

Explanation / Answer

inverse of cosine function is cos^-1 x

if we restrict the domain of cosine function

then , value of k would be 2pi

hence , option c is correct

2) perpendicular distance = 7 feet

base = 1.5 feet

applying tan rule on the triangle formed

tan theta = 7/1.5

theta = tan^-1 ( 7/1.5)

theta = 77.90 degrees

option a is correct

3) height = 15 feet

base = 12 feet

angle of inclination is

tan theta = 15/12

theta = tan^-1 ( 15/12 )

theta = 51.3 degrees

option a is correct

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