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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

User Rafe
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1 Answer

4 votes

Answer:

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

User Eka
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