Find the value of cos^(-1)(-1/2).

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Question: Find the value of cos^(-1)(-1/2).

Options:

Correct Answer: 2π/3

Solution:

cos^(-1)(-1/2) = 2π/3, since cos(2π/3) = -1/2.

Find the value of cos^(-1)(-1/2).

Find the value of cos^(-1)(-1/2).

Correct Answer: 2π/3

Step 1: Understand what cos^(-1)(-1/2) means. It is asking for the angle whose cosine value is -1/2.
Step 2: Recall the unit circle and the cosine values of common angles. The cosine of an angle is the x-coordinate of the point on the unit circle.
Step 3: Identify the angles where the cosine value is -1/2. These angles are 2π/3 and 4π/3.
Step 4: The range of the cos^(-1) function is from 0 to π (0 to 180 degrees). Therefore, we only consider the angle 2π/3.
Step 5: Conclude that cos^(-1)(-1/2) = 2π/3.

Inverse Trigonometric Functions – Understanding how to find angles using inverse cosine and recognizing the range of the function.
Unit Circle – Using the unit circle to determine the cosine values and their corresponding angles.