Question

HELP PLSS!!! 50PTS!!

Answer 1

`\sf cos(2\theta)=(31)/(49)`

Explanation:

Given that :

• 
  `\sf sin(\theta) = (3)/(7)`
• θ is in the first quadrant

We can use the following identity to find cos(2θ):

`\sf cos(2\theta) = 1 - 2 sin^2(\theta)`

Substituting value of sin(θ), we get:

`\sf cos(2\theta) = 1 - 2\left((3)/(7)\right)^2`

Evaluating, we get:

`\sf \sf cos(2\theta) = 1 - 2\left((9)/(49)\right)`

`\sf cos(2\theta) = 1 - \left((18)/(49)\right)`

`\sf cos(2\theta) = \left((1* 49-18)/(49)\right)`

`\sf cos(2\theta) = \left((31)/(49)\right)`

Therefore, the value of :

`\sf cos(2\theta)=(31)/(49)`