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)?

Question

6887 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-29T06:27:01

#sinx=sqrt(1-p^2)#

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

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

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)#