Problem

Acute angles \(A\) and \(B\) satisfy \(A+B=90°\). Use their complementary side roles in a right triangle to write \(\text{both}~\text{sine}\text{-}\text{cosine}~\text{cofunction}~\text{identities}\).

Prompt diagram of one right triangle with acute angles A and B. The angles are complementary, so A + B = 90 degrees; the legs switch opposite and adjacent roles when the reference changes from A to B. The identities are withheld.

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What this problem is really about

Complementary acute angles view the same two legs with opposite and adjacent roles reversed. We’ll establish the ninety-degree sum, track that role swap while keeping the hypotenuse fixed, derive one sine-cosine equality, and repeat the argument in the other direction.

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sin(A) = cos(B), but no second cofunction identity is needed.

sin(A) = cos(B) and cos(A) = sin(B) for any two angles.

sin(A) = cos(B) and cos(A) = sin(B), because A + B = 90°.

sin(A) = sin(B) and cos(A) = cos(B).

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Acute angles \(A\) and \(B\) satisfy \(A+B=90°\). Use their complementary side roles in a right triangle to write \(\text{both}~\text{sine}\text{-}\text{cosine}~\text{cofunction}~\text{identities}\).

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