Use the following information to determine sin(2x)? sin (x) = 2/3 and cos (x) is negative

Question

Solve step by step to get the answer

Answer 1

sin(2x) is a double-angle identity.

 

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

 

 

You can find cos(x) using the Pythagorean identity.

 

cos(x) = - √(1 - sin²(x))

 

 

sin(x) is already given to you.  Just plug it in to find cos(x).  Then multiply them together to get sin(2x).

 

sin(2x) = - 2sin(x)√(1 - sin²(x))