If sin(θ) = 1/√2, what is the value of θ in the range [0°, 360°]?
Practice Questions
1 question
Q1
If sin(θ) = 1/√2, what is the value of θ in the range [0°, 360°]?
45°, 225°
30°, 150°
60°, 300°
90°, 270°
sin(θ) = 1/√2 at θ = 45° and θ = 225°.
Questions & Step-by-step Solutions
1 item
Q
Q: If sin(θ) = 1/√2, what is the value of θ in the range [0°, 360°]?
Solution: sin(θ) = 1/√2 at θ = 45° and θ = 225°.
Steps: 5
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°.
