Question

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)?

Answer 1

`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)`