If pi/2≤θ≤π and sin θ =4/5, find the exact value of cosθ and cotθ?

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I tried doing this problem but got stuck midway through. I need some help finishing this problem

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Answer 1 · 2017-10-25T07:45:01

$cos(theta)= 3/5$

$cot(theta)=3/4$

First let's state what we know.

1). $sin^2(theta)+cos^2(theta)=1$

2). $sin(theta)/cos(theta)=tan(theta)$

3). $cot(theta)= 1/tan(theta)$

So we have:

$(4/5)^2+cos^2(theta)=1=>cos^2(theta)=1-16/25=9/25$

$->cos^2(theta)=9/25$

Taking roots:

$cos(theta)= (sqrt(9))/(sqrt(25))=color(blue)(3/5)$

$cot(theta)= (1)/((sin(theta))/(cos(theta)))=1/((4/5)/(3/5))=1/(4/3)=color(blue)(3/4)$