If sin ⁡x=7/25, and 0<x<π/2, what is tan⁡(x−π/4)?

Question

Help please.

If sin ⁡x=7/25, and 0<x<π/2, what is tan⁡(x−π/4)?

Answer 1

Take the inverse SIN x = 7/25. 7/25 is 0.28. x = INVSIN x(O.28) = 16.26 Degrees.

You need to convert Degrees to Radians when using PI. x = 16.26 x PI /180 = 0.2837 Radians

So Tan (0.2837 - PI/4) = Tan(0.2837 - 0.7854) - Tan(-0.5017) = -0.5485

Answer 2

Consider the trig identity

tan(x - π/4) = (tan(x) - tan(π/4)/(1 + tan(x)tan(π/4)) = (tan(x) - 1)/(1 + tan(x))

since tan(π/4) = 1

So we need the value of tan(x) which can be calculated as follows

tan² (x) = sin² (x)/cos² (x) = (7/25)²/(1 - (7/25)²) = 49/576 ⇒ tan(x) = 7/24

The -7/24 root is not acceptable since x is between 0 and π/2, i.e. in the first quadrant. Hence,

tan(x - π/4) = (tan(x) - 1)/(1 + tan(x)) = (7/24 - 1)/(1 + 7/24) = -17/31