What is the value of arcsin(x) + arccos(x) for all x in [-1, 1]?
Answer and explanation
Correct answer: B. pi / 2
- Step 1: Let theta = arcsin(x), so sin(theta) = x. Then cos(pi/2 - theta) = sin(theta) = x. Step 2. Thus arccos(x) = pi/2 - theta, meaning arcsin(x) + arccos(x) = pi/2. Answer: pi / 2. Why not the others: pi is 180 degrees; 0 would mean equal opposite values; pi/4 holds only at x = 1/root 2.
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