Question

If StartFraction pi Over 2 EndFraction less than t less than pi ​, which of the following is​ true?

a. cosine t less than 0 and cotangent t less than 0
b. cosine t less than 0 and cotangent t greater than 0
c. cosine t greater than 0 and cotangent t less than 0
d. cosine t greater than 0 and cotangent t greater than 0

Answer 1

b. cosine t less than 0 and cotangent t greater than 0

Explanation:

We have the following relation

`(\pi )/(2) < t <\pi`

if we apply the cosine function in the relation we get:

`cos(\pi )/(2) <cost<cos\pi`

`-1<cost<0`

the cosine of t is between 0 and -1 then (cosine t less than 0)

If we now apply cotangent function in the relation:

`cotan(\pi )/(2) <cotan(t)<cotan\pi`

`0 <cotan(t)<\infty`

This means that cotang is greater than 0, therefore the correct answer is b. cosine t less than 0 and cotangent t greater than 0