Eric Nicholas K's answer to There's a feeling's Secondary 4 A Maths Singapore question.

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Eric Nicholas K
Eric Nicholas K's answer
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To get our R cos (theta - alpha), we must first position our function as a cos theta + b sin theta, where a and b are positive numbers.

Then, R = square root of (a^2 + b^2) like Pythagoras theorem.

Alpha is taninv of (b/a), where alpha is an acute angle.

For maximum value, we set cos (theta + alpha) to 1, because for any cosine function, -1 <= cos (...) <= 1.