Question

If cosx=y, find sin(x-pi/2)

Answer 1

Use the cofunction identity:

sin(pi/2-u)=cos(u)

And the fact that: sin(u-pi/2)=sin[-(pi/2-u)]

And the fact that sin(-z)=-sin(z) since sine is an odd function.

Answer 2

either you can use
\[\sin \left( A-B \right)=\sin A \cos B-\cos A \sin B\]

Answer 3

^^^But @surjithayer wouldn't you need to know sin(x) to use that identity?

Answer 4

\[\sin \left( x-\frac{ \pi }{ 2 } \right)=\sin x \cos \frac{ \pi }{ 2 }-\cos x \sin \frac{ \pi }{ 2 }\]
\[\cos \frac{ \pi }{2 }=0,\sin \frac{ \pi }{ 2 }=1\]

Answer 5

Oh right, the term with the sin(x) goes away, since it is multiplied by 0. Good point. :)