Evaluate sin^(-1)(-1/2) + cos^(-1)(1/2).

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Question: Evaluate sin^(-1)(-1/2) + cos^(-1)(1/2).

Options:

Correct Answer: π/2

Solution:

sin^(-1)(-1/2) = -π/6 and cos^(-1)(1/2) = π/3. Therefore, -π/6 + π/3 = π/6.

Evaluate sin^(-1)(-1/2) + cos^(-1)(1/2).

Evaluate sin^(-1)(-1/2) + cos^(-1)(1/2).

Step 1: Understand the notation. sin^(-1)(-1/2) means the angle whose sine is -1/2.
Step 2: Recall the unit circle. The sine of an angle is negative in the fourth quadrant.
Step 3: Find the angle where sine is -1/2. This angle is -π/6 (or -30 degrees).
Step 4: Now, look at cos^(-1)(1/2). This means the angle whose cosine is 1/2.
Step 5: Recall that cosine is positive in the first quadrant. The angle where cosine is 1/2 is π/3 (or 60 degrees).
Step 6: Now, combine the two results: -π/6 + π/3.
Step 7: To add these fractions, convert π/3 to have a common denominator with -π/6. π/3 = 2π/6.
Step 8: Now add: -π/6 + 2π/6 = (2π - π)/6 = π/6.
Step 9: The final answer is π/6.

Inverse Trigonometric Functions – Understanding the values of sin^(-1) and cos^(-1) for specific angles.
Angle Addition – Combining angles from inverse trigonometric functions to find a resultant angle.