Question

If cos0=3/5 and θ is in quadrant IV, sin20=?

Answer 1

`sen(2\theta) =(24)/(25)`

Explanation:

We know that
`cos(\theta) =(3)/(5)` and θ is in quadrant IV

To find
`sin(\theta)` we use the following identity

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

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

`cos^2(\theta) =(9)/(25)`

Then

`sin^2(\theta)=1-(9)/(25)`

`sin^2(\theta)=(16)/(25)`

`sin(\theta)=\±\sqrt{(16)/(25)}`

In the IV quadrant the
`sin(\theta)> 0` then we take the positive solution

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

Finally to find
`sin(2\theta)` we use the following identity

`sen(2\theta) = 2 sen(\theta) cos(\theta)`

Finally

`sen(2\theta) = 2*(4)/(5)*(3)/(5)`

`sen(2\theta) =(24)/(25)`