Given that sin(90 -5thetha) = Cos(180 - 0),
Find the value of theta

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:

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

final answer is : )