simplify sin(540-2x)
this is to do with trig
sin(540-2x) = sin(360+180-2x)
= sin(180-2x)
= sin(2x)
To simplify the expression sin(540 - 2x), we can use the angle subtraction identity for sine. According to this identity, sin(a - b) = sin(a)cos(b) - cos(a)sin(b).
In this case, let's substitute a = 540 and b = 2x into the identity.
sin(540 - 2x) = sin(540)cos(2x) - cos(540)sin(2x)
Now, we need to determine the values of sin(540) and cos(540). To do this, we can use the fact that the sine and cosine functions have periodicity of 360 degrees. As such, sin(540) = sin(540 - 360) and cos(540) = cos(540 - 360).
sin(540) = sin(540 - 360) = sin(180) = 0
cos(540) = cos(540 - 360) = cos(180) = -1
With these substitutions, the expression becomes:
sin(540 - 2x) = 0 * cos(2x) - (-1) * sin(2x)
sin(540 - 2x) = 0 + sin(2x)
sin(540 - 2x) = sin(2x)
Hence, the simplified form of sin(540 - 2x) is sin(2x).