Solve for v:
cos(π/4+v) = -1/sqrt(2)
Take the inverse cosine of both sides:
π/4+v = (3 π)/4+2 π n_1 for n_1 element Z
or π/4+v = (5 π)/4+2 π n_2 for n_2 element Z
Subtract π/4 from both sides:
v = π/2+2 π n_1 for n_1 element Z
or π/4+v = (5 π)/4+2 π n_2 for n_2 element Z
Subtract π/4 from both sides:
Answer: |v = π/2+2 π n_1 for n_1 element Z
or v = π+2 π n_2 for n_2 element Z