Question

Given tan∅=4/3 and π<∅<(3π)/2; find cos2∅

a. -24/25
b. 24/25
c. -24/7
d. -7/25

Answer 1

`cos(2\theta)=-(7)/(25)`

Explanation:

we are given

`tan(\theta)=(4)/(3)`

Firstly, we will draw triangle

Since, angle lies in third quadrant

so,

`sin(\theta)=-(4)/(5)`

`cos(\theta)=-(3)/(5)`

now, we can sue formula

`cos(2\theta)=cos^2(\theta)-sin^2(\theta)`

now, we can plug values

`cos(2\theta)=(-(3)/(5))^2-(-(4)/(5))^2`

we can simplify it

`cos(2\theta)=-(7)/(25)`