Question

Find 2 given that =−4/5 and < < 3/2

Answer 1

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

`\sin ^2(x)+\cos ^2(x)=1^{}`

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)

`\begin{gathered} (-(4)/(5))^2+\cos ^2(x)=1^{} \\ \\ (16)/(25)+\cos ^2(x)=1^{} \\ \\ \cos ^2(x)=1-(16)/(25) \\ \cos ^2(x)=(9)/(25) \\ \cos (x)=-(3)/(5) \end{gathered}`

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)

sin(2x)=24/25