Explain and use the complementary-angle relationship between sine and cosine.
Solve a sine-cosine equation by using complementary acute angles
Problem
Angles \(3x°\) and \(60°\) are acute and satisfy \(\sin(3x°)=\cos(60°)\). Use the cofunction relationship to set \(3x+60=90\), then solve for \(x\).
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What this problem is really about
For acute angles, equal sine and cosine values signal complementary arguments rather than equal arguments. We’ll convert the cofunction equation into a ninety-degree angle sum, solve the resulting linear equation, and substitute back to verify both special-angle trig values.
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