If cos(θ) = 1/2, what are the possible values of θ in the range [0°, 360°]?

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Question: If cos(θ) = 1/2, what are the possible values of θ in the range [0°, 360°]?

Options:

Correct Answer: 60°, 300°

Solution:

cos(θ) = 1/2 at θ = 60° and θ = 300°.

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°]?

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°.

Trigonometric Functions – Understanding the values of cosine and their corresponding angles in the unit circle.
Inverse Trigonometric Functions – Using the inverse cosine function to find angles that yield a specific cosine value.
Angle Measurement – Identifying angles in degrees within a specified range.