Question

Question #a6063

Answer 1

`sin 2 theta = 2 sin theta cos theta`
`=2 (3/7)((2sqrt10)/7)`
`=(12sqrt10)/49`

Explanation:

`sin(2csc^-1 (7/3))`.

First we use `csc^-1 (7/3))` to draw a triangle with hypotenuse 7 and opposite 3 . Then we can find the missing side by using pythagorean theorem. That is, adjacent = `sqrt(h^2-o^2)=sqrt(7^2 - 3^2) = sqrt(49-9)=sqrt40 = 2sqrt10`

Now we need to find `sin 2 theta` by using the double angle
formula

`sin 2 theta = 2 sin theta cos theta`
`=2 (3/7)((2sqrt10)/7)`
`=(12sqrt10)/49`