Q:

If 0° < θ < 90°, is sin θ equal to cos (90° – θ), and for what reason?A) No, because angles measuring θ and 90° – θ are supplements. B) No, because angles measuring θ and 90° – θ are complements. C) Yes, because angles measuring θ and 90° – θ are supplements. D) Yes, because angles measuring θ and 90° – θ are complements.

Accepted Solution

A:
Answer:Option D. Yes, because angles measuring [tex](\theta)[/tex]  and [tex](90\°-\theta)[/tex]  are complementsStep-by-step explanation:we know thatTwo angles are complementary if their sum is equal to [tex]90[/tex] degreesandIf two angles are complementary, then the function sine of one angle is equal to the function cosine of the other angle thereforeIn this problem[tex](\theta)+(90\°-\theta)=90\°[/tex] so[tex](\theta)[/tex]  and [tex](90\°-\theta)[/tex] -----> are complementary angleshence[tex]sin(\theta)=cos(90\°-\theta)[/tex]