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If cos(θ) = 1/2, what are the possible values of θ in the range [0°, 360°]?
If cos(θ) = 1/2, what are the possible values of θ in the range [0°, 360°]?
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Practice Questions
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Q1
If cos(θ) = 1/2, what are the possible values of θ in the range [0°, 360°]?
60°, 300°
30°, 150°
90°, 270°
0°, 180°
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cos(θ) = 1/2 at θ = 60° and θ = 300°.
Questions & Step-by-step Solutions
1 item
Q
Q: If cos(θ) = 1/2, what are the possible values of θ in the range [0°, 360°]?
Solution:
cos(θ) = 1/2 at θ = 60° and θ = 300°.
Steps: 5
Show Steps
Step 1: Understand that cos(θ) = 1/2 means we are looking for angles where the cosine value is 1/2.
Step 2: Recall the unit circle and the special angles. The cosine of an angle corresponds to the x-coordinate on the unit circle.
Step 3: Identify the angles where cos(θ) = 1/2. These angles are 60° and 300°.
Step 4: Check that both angles are within the range of [0°, 360°]. 60° is in the range, and 300° is also in the range.
Step 5: Conclude that the possible values of θ are 60° and 300°.
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