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If cos(θ) = 1/2, what are the possible values of θ?
If cos(θ) = 1/2, what are the possible values of θ?
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Practice Questions
1 question
Q1
If cos(θ) = 1/2, what are the possible values of θ?
30°, 150°
45°, 135°
60°, 120°
0°, 180°
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cos(θ) = 1/2 at θ = 30° and 150°.
Questions & Step-by-step Solutions
1 item
Q
Q: If cos(θ) = 1/2, what are the possible values of θ?
Solution:
cos(θ) = 1/2 at θ = 30° and 150°.
Steps: 6
Show Steps
Step 1: Understand that cos(θ) = 1/2 means we are looking for angles θ where the cosine value is 1/2.
Step 2: Recall the unit circle, which helps us find angles based on their cosine values.
Step 3: Remember that cos(θ) = 1/2 corresponds to specific angles in the first and second quadrants.
Step 4: Identify the first angle where cos(θ) = 1/2, which is 30°.
Step 5: Identify the second angle where cos(θ) = 1/2, which is in the second quadrant, specifically 180° - 30° = 150°.
Step 6: Conclude that the possible values of θ are 30° and 150°.
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