If sin(θ) = 1/√2, what is the value of θ in the range [0°, 360°]?

If sin(θ) = 1/√2, what is the value of θ in the range [0°, 360°]?

Step 1: Understand that sin(θ) = 1/√2 means we are looking for angles where the sine value is equal to 1/√2.
Step 2: Recall that sin(θ) = 1/√2 is a known value that corresponds to specific angles in the unit circle.
Step 3: The first angle where sin(θ) = 1/√2 is 45° (or π/4 radians).
Step 4: The sine function is positive in the first and second quadrants. The second angle where sin(θ) = 1/√2 is found by adding 180° to 45°, which gives us 225° (or 5π/4 radians).
Step 5: Therefore, the two angles in the range [0°, 360°] where sin(θ) = 1/√2 are 45° and 225°.

Trigonometric Functions – Understanding the sine function and its values at specific angles.
Unit Circle – Using the unit circle to determine angles corresponding to specific sine values.
Quadrants of Angles – Recognizing that sine is positive in the first and second quadrants.