Solve each equation for 0 ≤ 𝜃 < 2𝜋. Give exact answers. Enter your answers as a comma-separated list if needed. sin 𝜃 = 1

Question

Solve each equation for 0 ≤ 𝜃 < 2𝜋. Give exact answers. Enter your answers as a comma-separated list if needed.

sin 𝜃 = 1

cos 𝜃 = −1

sin 𝜃 = 0

cos 𝜃 = 1

sin 𝜃 = −1

cos 𝜃 = 0

Answer 1

sinθ = 1; θ = π/2.

cosθ = - 1; θ = π.

sinθ = 0, θ = 0 or θ = π.

cosθ = 1, θ = 0.

sinθ = - 1, θ = 3π/2.

cosθ = 0, θ = π/2 or θ = 3π/2.

Answer 2

All exact values for sine and cosine are located on a unit circle where x = cos𝜃  and y = sin𝜃. Values where sine and cosine are equal to -1, 1, or zero are located at 0, 90, 180, 270, or 360 degrees since the radius of a unit circle is 1. Do you know what the answers are now?

For sin𝜃 = 1 look for a y-coordinate of 1 and then your answer is the angle. What is the answer?