Question

Given cos(O) =1/3
Find cos(2O)

Answer 1

`\displaystyle \cos 2\theta=-(7)/(9)`

Explanation:

Cosine Double Angle

Given the cosine of an angle θ, the cosine of 2θ is given by the formula:

`\cos 2\theta=2\cos^2\theta-1`

Given

`\displaystyle \cos \theta=(1)/(3)`

Calculate

`\displaystyle \cos 2\theta=2\left((1)/(3)\right)^2-1`

`\displaystyle \cos 2\theta=2\left((1)/(9)\right)-1`

`\displaystyle \cos 2\theta=(2)/(9)-1=-(7)/(9)`

`\mathbf{\displaystyle \cos 2\theta=-(7)/(9)}`