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Find the maximum and minimum values of 5*cos(theta) + 3*sin(theta + pi/6) over all real theta.

1. Maximum 7, minimum -7
2. Maximum 8, minimum -8
3. Maximum sqrt(34), minimum -sqrt(34)
4. Maximum 4, minimum -4

Correct answer: Maximum 7, minimum -7

Solution

Expanding gives (13/2)cos theta + (3 sqrt(3)/2) sin theta, whose amplitude is sqrt((13/2)² + (3 sqrt(3)/2)²) = sqrt(196/4) = 7.

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