Question

If sin theta 3/5 and theta terminates in the first quadrant find the exact value of cos 2 theta

Answer 1

`cos2\theta =(7)/(25)`

Explanation:

We have

`sin\theta =(3)/(5)`

We know

sin²θ + cos²θ = 1

`\left ((3)/(5) \right )^2+cos^2\theta =1\\\\cos^2\theta =(16)/(25)\\\\cos\theta =(4)/(5)`

We need to find cos2θ

We have

cos2θ = cos²θ - sin²θ

`cos2\theta =\left ((4)/(5) \right )^2-\left ((3)/(5)\right )^2=(7)/(25)`