To find the exact values of cos(3π/4) and sin(3π/4), we first recognize that 3π/4 is in the second quadrant of the unit circle.
In the second quadrant, the cosine value is negative, while the sine value is positive. The reference angle for 3π/4 can be found by subtracting it from π:
π - 3π/4 = π/4
Now we can use the known values at the reference angle π/4, which are:
cos(π/4) = √2/2sin(π/4) = √2/2
Therefore, applying the sign based on the quadrant for 3π/4:
cos(3π/4) = -cos(π/4) = -√2/2sin(3π/4) = sin(π/4) = √2/2
Hence, the exact values are:
cos(3π/4) = -√2/2
sin(3π/4) = √2/2