Find 2 given that =−4/5 and < < 3/2

Find 2 given that =

−4/5 and < < 3/2

we know that

sin(2x) = 2 sin(x) cos(x)

so

step 1

Find the value of cos(x)

Remember that

we have

sin(x)=-4/5

The angle x lies on III quadrant

that means

cos(x) is negative

substitute the value of sin(x)

step 2

Find the value of sin(2x)

sin(2x) = 2 sin(x) cos(x)

we have

sin(x)=-4/5

cos(x)=-3/5

substitute

sin(2x)=2(-4/5)(-3/5)

the answer to this question is in the pic