The formula for sin(2x)
sin(2x) = 2 sin(x) cos(x)
Where
- x is an angle in radians and
- sin and cos are the sine and
- cosine functions, respectively.
The formula expresses the sine of 2x in terms of the sine and cosine of x.
The formula can be derived from the addition formula for sine:
- sin(A + B) = sin(A) cos(B) + cos(A) sin(B)
- By setting A = x and B = x, we get:
- sin(2x) = sin(x) cos(x) + cos(x) sin(x) = 2 sin(x) cos(x)
So, the formula for sin(2x) is equal to 2 times the product of the sine and cosine of x.