AIR MATH

Math Question

Malia tried to prove that \( \cos (\theta)=\sin \left(90^{\circ}-\theta\right) \) using the following diagram. Her proof is not correct. Statement Reason \( 1 \quad m \angle C=90^{\circ}-\theta \quad \) The acute angles in a right triangle are complementary. \( 2 \sin \left(90^{\circ}-\theta\right)=\frac{A C}{B C} \quad \) Definition of sine. \( 3 \cos (\theta)=\frac{A C}{B C} \quad \) Definition of cosine. \( 4 \cos (\theta)=\sin \left(90^{\circ}-\theta\right) \quad \) Substitution What is the first mistake in Malia's proof?

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