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If cos(θ) = 1/2, what are the possible values of θ in degrees?
If cos(θ) = 1/2, what are the possible values of θ in degrees?
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Practice Questions
1 question
Q1
If cos(θ) = 1/2, what are the possible values of θ in degrees?
30, 150
45, 135
60, 120
0, 180
Show Solution
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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 in degrees?
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 and the special angles. The cosine of an angle corresponds to the x-coordinate on the unit circle.
Step 3: Identify the angles where the cosine value is 1/2. These angles are 30° and 150°.
Step 4: Remember that cosine is positive in the first and fourth quadrants. Since 30° is in the first quadrant, it is one solution.
Step 5: The second solution is found in the second quadrant, which is 180° - 30° = 150°.
Step 6: Conclude that the possible values of θ are 30° and 150°.
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