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Evaluate tan⁻¹(1) + cos⁻¹(-1/2) + sin⁻¹(-1/2).

1. pi/4
2. 5*pi/12
3. 3*pi/4
4. 13*pi/12

Correct answer: 3*pi/4

Solution

tan⁻¹(1) = pi/4. cos⁻¹(-1/2) = pi - pi/3 = 2*pi/3. sin⁻¹(-1/2) = -pi/6. Sum = pi/4 + 2*pi/3 - pi/6. LCD 12: = 3*pi/12 + 8*pi/12 - 2*pi/12 = 9*pi/12 = 3*pi/4.

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