Question

DUE TODAY PLEASE HELP!!!!

For which angles is the cosine positive? Select all that apply.

a
0 radians
b
5π/12 radians
c
5π/6 radians
d
3π/4 radians
e
5π/3 radians

Answer 1

Explanation:

if it is between 0 and pi/2 (90°), or between 3pi/2 (270°) and 2pi (360°).

for angle = 0, cos = 1. therefore, positive.

0 <= 5pi/12 <= pi/2. therefore, positive.

pi/2 <= 5pi/6 <= pi. therefore, negative.

pi/2 <= 3pi/4 <= pi. therefore, negative.

3pi/2 <= 5pi/3 <= 2pi. therefore, positive.

you do know how to compare fractions, right ?

you need to bring then to the same denominator by multiplying numerator and denominator by the same factor.

e.g. comparing 5pi/12 with pi/2.

to bring them both to .../12, we have to multiply pi/2 by 6/6.

so, we are comparing 5pi/12 and 6pi/12.

and we see, 5pi/12 is smaller.

the others work the same way.

3pi/6 <= 5pi/6 <= 6pi/6

2pi/4 <= 3pi/4 <= 4pi/4

9pi/6 <= 10pi/6 <= 12pi/6

now you see it clearly.