Given that cosx=p Where x us an acute angle in degrees find in term of p i) Sin x ii)tanx iii)tan(90-x)?

1 Answer
Apr 29, 2018

sinx=sqrt(1-p^2)

tanx=(sqrt(1-p^2))/p

tan(90-x)=p/sqrt(1-p^2)

Explanation:

The Pythagorean theorem states

sin^2x+cos^2x=1

Solving for sinx we have

sin^2x=1-cos^2x

sinx=sqrt(1-cos^2x)

If

cosx=p,

then

sinx=sqrt(1-p^2),

tanx=sinx/cosx=(sqrt(1-p^2))/p,

and

tan(90-x)=sin(90-x)/cos(90-x)=cosx/sinx=p/sqrt(1-p^2)