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

Question

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

I really need help

Answer 1

cos(x-3pi/2) = about .28

x =sin^-1(7/25) = sin^-1(.28) = about 16.26

3pi/2 = 270 degrees

cos(x-270) = about cos(16.26-270) = cos(90-16.26) = cos73.74 = .28

use a calculator with trig functions

or another approach

sinx = 7/25 = o/h = opposite side over hypotenuse

given 0<sinx< sqr2/2 = about .707, 0<x<45 degrees

cosx = 24/25 = a/h = adjacent side over hypotenuse

cos(x -3pi/2) = cos(x -270 degrees)

= cosxcos270 - sinxsin270 = cosx(0) - sinx(1) = -sinx = -1 sinx = 1

x = 90 degrees = pi radians but it's given in the problem that 0<x< pi/2 and pi is Not less than pi/2