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)#