Question

If sin ⁡x=7/25, and 0 < x < π/2, what is cos⁡(x−3π/2)?

Answer 1

`Cos(x-(3\pi)/(2))=-(7)/(25)`

Explanation:

Remember that
`cos(x-y)=cos(x)cos(y)+sin(x)sin(y)`

Then,

`cos(x-(3\pi)/(2))=cos(x)cos((3\pi)/(2))+sin(x)sin((3\pi)/(2))\\`

But
`cos((3\pi)/(2))=0` and
`sin(x)=(7)/(25)`

Then

`cos(x-(3\pi)/(2))=cos(x)*0+(7)/(25)*sin((3\pi)/(2))\\=(7)/(25)*(-1)=(-7)/(25)`