Answer:
θ = 54 - π/10 - (2 π n_1)/5 for n_1 element Z
or θ = -18 - π/10 - (2 π n_2)/5 for n_2 element Z
Step-by-step explanation:
Solve for θ:
sin(90 - 5 θ) = cos(180)
Hint: | Express the right hand side in terms of sine.
Rewrite the right hand side using cos(θ) = sin(θ + π/2):
sin(90 - 5 θ) = sin(π/2 + 180)
Hint: | Eliminate the sine from the left hand side.
Take the inverse sine of both sides:
90 - 5 θ = -180 + π/2 + 2 π n_1 for n_1 element Z
or 90 - 5 θ = 180 + π/2 + 2 π n_2 for n_2 element Z
Hint: | Look at the first equation: Isolate terms with θ to the left hand side.
Subtract 90 from both sides:
-5 θ = -270 + π/2 + 2 π n_1 for n_1 element Z
or 90 - 5 θ = 180 + π/2 + 2 π n_2 for n_2 element Z
Hint: | Solve for θ.
Divide both sides by -5:
θ = 54 - π/10 - (2 π n_1)/5 for n_1 element Z
or 90 - 5 θ = 180 + π/2 + 2 π n_2 for n_2 element Z
Hint: | Look at the second equation: Isolate terms with θ to the left hand side.
Subtract 90 from both sides:
θ = 54 - π/10 - (2 π n_1)/5 for n_1 element Z
or -5 θ = 90 + π/2 + 2 π n_2 for n_2 element Z
Hint: | Solve for θ.
Divide both sides by -5:
Answer: θ = 54 - π/10 - (2 π n_1)/5 for n_1 element Z
or θ = -18 - π/10 - (2 π n_2)/5 for n_2 element Z
