if f(x) = sin4x-cos2x, find f(pi/8)

simply plug in (pi/8) wherever you see x and sovel

*solve

sin(π/2) - cos(π/4)

= 1 - √2/2
= (2-√2)/2

*solve

To find the value of f(pi/8), we need to substitute pi/8 into the function f(x) = sin(4x) - cos(2x).

We can break down the calculation into two steps. First, substitute pi/8 into sin(4x) part of the function, then subtract the value of cos(2x) when x = pi/8.

Step 1: Substitute pi/8 into sin(4x)
sin(4(pi/8)) = sin(2pi/2) = sin(pi) = 0

Step 2: Calculate the value of cos(2x) when x = pi/8
cos(2(pi/8)) = cos(pi/4) = 1/sqrt(2) or (√2)/2

Now, substitute the values we found back into the original function:
f(pi/8) = 0 - (√2)/2

Therefore, f(pi/8) = -(√2)/2 or approximately -0.707.