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

I tried doing this problem but got stuck midway through. I need some help finishing this problementer image source here

1 Answer
Oct 25, 2017

cos(theta)= 3/5

cot(theta)=3/4

Explanation:

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)