Given tan x 56 32

Given tan x = -⁵/₆, ³/₂<x<2, use trigonometric identities to find sin x and cos x

Solution

Q) Given tan x = -⁵/₆, ³/₂<x<2, use trigonometric identities to find sin x and cos x

Tax x = -5/6     => sinx/ cosx = -5/6

Using Trigonometric Functions we know that,

Sin^2x + Cos^2x = 1                                               Equation 2

Applying the above Cosx value from equation 1 to equaton 2, we get;

Sin^2x + (-6/5Sinx)^2= 1

We already know that x lies in 4^th Quadrant i.e. x lies in ³/₂<x<2

Hence, Sinx = -5/7   In this quadrant, all sin values are negative.

Tanx = Sinx/Cosx

Hence, Cosx = Sinx/Tanx

Cos value is always positive in 4^th quadrant.

Ans:              

Sinx = -5/7

Cosx = 6/7