Question

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

Answer 1

Answer:

$Cos(x-\frac{3\pi}{2})=-\frac{7}{25}$

Step-by-step explanation:

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

Then,

$cos(x-\frac{3\pi}{2})=cos(x)cos(\frac{3\pi}{2})+sin(x)sin(\frac{3\pi}{2})$

But $cos(\frac{3\pi}{2})=0$ and $sin(x)=\frac{7}{25}$

Then

$cos(x-\frac{3\pi}{2})=cos(x)*0+\frac{7}{25}*sin(\frac{3\pi}{2})\\=\frac{7}{25}*(-1)=\frac{-7}{25}$