Evaluate cos^(-1)(0).

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Question: Evaluate cos^(-1)(0).

Options:

Correct Answer: π

Solution:

cos^(-1)(0) = π, since cos(π) = 0.

Evaluate cos^(-1)(0).

Evaluate cos^(-1)(0).

Step 1: Understand what cos^(-1)(0) means. It is asking for the angle whose cosine value is 0.
Step 2: Recall the unit circle, which helps us understand the values of cosine for different angles.
Step 3: Identify the angles where the cosine value is 0. These angles are π/2 (90 degrees) and 3π/2 (270 degrees).
Step 4: However, the function cos^(-1) (also known as arccos) only gives us values in the range from 0 to π (0 to 180 degrees).
Step 5: Since we are looking for the angle in this range, we find that cos(π/2) = 0.
Step 6: Therefore, cos^(-1)(0) = π/2.

Inverse Trigonometric Functions – Understanding how to evaluate inverse cosine and the values it can take.
Unit Circle – Knowledge of the unit circle and the angles corresponding to specific cosine values.