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Answer:
α = -2 π n_1 - π/2 for n_1 element Z
or α = -2 π n_2 - π/6 for n_2 element Z
Step-by-step explanation:
Solve for α:
sin(-α + π/6) = sqrt(3)/2
Hint: | Eliminate the sine from the left hand side.
Take the inverse sine of both sides:
-α + π/6 = 2 π n_1 + (2 π)/3 for n_1 element Z
or -α + π/6 = 2 π n_2 + π/3 for n_2 element Z
Hint: | Look at the first equation: Isolate terms with α to the left hand side.
Subtract π/6 from both sides:
-α = 2 π n_1 + π/2 for n_1 element Z
or -α + π/6 = 2 π n_2 + π/3 for n_2 element Z
Hint: | Solve for α.
Multiply both sides by -1:
α = -2 π n_1 - π/2 for n_1 element Z
or -α + π/6 = 2 π n_2 + π/3 for n_2 element Z
Hint: | Look at the second equation: Isolate terms with α to the left hand side.
Subtract π/6 from both sides:
α = -2 π n_1 - π/2 for n_1 element Z
or -α = 2 π n_2 + π/6 for n_2 element Z
Hint: | Solve for α.
Multiply both sides by -1:
Answer: α = -2 π n_1 - π/2 for n_1 element Z
or α = -2 π n_2 - π/6 for n_2 element Z