If sinθ =4/7, what is cosθ?

3 Answers
Jun 20, 2018

cosθ= +- 33^(1/2)/7

Explanation:

Since

Sin^2θ xx cos^2θ =1

you have

(4/7)^2 xx cos^2θ=1

So

Cos^2θ= 1- 16/49

Cosθ= +- 33^(1/2)/7

Jun 20, 2018

cos(theta)=+-sqrt(33)/7

Explanation:

We want to find cos(theta), when sin(theta)=4/7

By the pythagorean trig identity

color(blue)(cos^2(theta)+sin^2(theta)=1

=>cos^2(theta)=1-sin^2(theta)

=>cos(theta)=+-sqrt(1-sin^2(theta))

Substitute color(red)(sin(theta)=4/7

cos(theta)=+-sqrt(1-(4/7)^2)

color(white)(cos(theta))=+-sqrt(1-(16/49)

color(white)(cos(theta))=+-sqrt((49-16)/49)

color(white)(cos(theta))=+-sqrt(33)/7

Jun 20, 2018

cos(theta)=pmsqrt(33)/7

Explanation:

Using the relation
sin^2(theta)+cos^2(theta)=1 then we get
cos(theta)=pmsqrt(1-16/49)