If cos(θ) = 1/2, what are the possible values of θ in degrees?

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Question: If cos(θ) = 1/2, what are the possible values of θ in degrees?

Options:

Correct Answer: 30, 150

Solution:

cos(θ) = 1/2 at θ = 30° and 150°.

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?

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°.

Trigonometric Functions – Understanding the values of trigonometric functions, specifically the cosine function, and their corresponding angles.
Unit Circle – Knowledge of the unit circle and how it relates to the angles where cosine takes specific values.
Quadrants – Recognizing that cosine is positive in the first and fourth quadrants, leading to multiple angle solutions.