Answer to Question #157034 in Trigonometry for Kinza Tahir

Question

Determine the value of sin2x given that tan^2x=81/49 and Pi<x<3pi/2

Answer 1

$tan²x = \frac{81}{49}$

=> $tan x = \frac{9}{7}$

$x = tan^{-1} (\frac{9}{7}) x = 52.1250^{0}$

Since tan is positive in both 1st and 3rd quadrant, that implies

In 1st quadrant

x = 52.1250°

In the 3rd quadrant

x = 180 + 52.1250° = 232.1250°

But $π<x<\frac{3π}{2}$

Therefore, x = 232.1250°

$Sin 2x = Sin 2(232.1250) = 0.9692$