Cos(alpha + pi/3) = (sqrt(3))/2

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:

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

c. side angle side. u shares the same sides