Explain and use the complementary-angle relationship between sine and cosine.
Rewrite sine of an acute angle as cosine of its complement
Problem
Compute the complement of \(30°\) and use \(\sin(θ)=\cos(90°-θ)\) to rewrite \(\sin(30°)\) as a cosine expression.
Big Picture
What this problem is really about
Rewriting a trig function with its cofunction requires changing to the complementary angle at the same time. We’ll compute ninety degrees minus the given angle, apply the sine-to-cosine identity, and verify the rewrite by comparing the two exact special-angle values.
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