cos(x)=12/13 solve for sin(2x)

Question

solve for sin(2x)

Answer 1

If cos(x) = 12/13  so one side of the triangle is 12 and the hypotenuse is 13, so the other side is:

 

√(13² - 12²) = √25 = 5

 

so sin(x) = 5/13

 

Now use the double angle identity:

 

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

sin(2x) = 2(5/13)(12/13) = ____?