If sin theta = sqrt (2/2), which could not be the value of theta?

-225 degrees

-45 degrees

-135 degrees

-405 degrees

The solution would be like this for this specific problem:

sin (θ°) = √ (2) / 2

θ° = 360°n + sin⁻¹ (√ (2) / 2) and θ° = 360°n + 180° - sin⁻¹ (√ (2) / 2)

θ° = 360°n + 45° and θ° = 360°n + 135° where n∈ℤ

360°*0 + 45° = 45°

360°*0 + 135° = 135°

360°*1 + 45° = 405°

sin (225°) = - √ (2) / 2

225 has an angle where sin theta = - (sqrt2) / 2 therefore, the value of theta cannot be 225 degrees.