Find all angles θ that make the equation sin (θ) = 1/√2 a true equation.

Answer 1

I would just add that you get other solutions by going around the circle in either direction. So the full solution would be the set of all values of the form π/4 + 2πn or 3π/4 +2πn for some integer n.

Answer 2

sinθ= 1/√2; θ = (-1)ⁿ·π/4 + πn

Answer 3

I am assuming you are familiar with the unit circle. Recall that on the unit circle, sin(θ) is the y-coordinate. So you want to find the point(s) on the unit circle where the y-coordinate is 1/√2. Note that if you rationalize the denominator, this is written as √2/2, so you could see either one of these depending on how the values on your unit circle are written. You should see two points where the y-coordinate is 1/√2. The first one corresponds to the angle π/4 and the other point corresponds to the angle 3π/4. So the angles (values of θ) that make this equation true are π/4 and 3π/4.