7.8k views
0 votes
Verify this cofunction identity by using the difference identity for cosine. Show your work! cos⁡(π/2-θ)=sinθ

1 Answer

4 votes
cos(A-B) = cosAcosB + sinAsinB

cos(π/2 - θ) = cos(π/2)cosθ + sin(π/2)sinθ

π/2 = 90°
cos(π/2) = cos90° = 0. sin(π/2) = sin90° = 1

cos(π/2 - θ) = cos(π/2)cosθ + sin(π/2)sinθ

= 0*cosθ + 1*sinθ = sinθ

Therefore
cos(π/2 - θ) = sinθ

QED

User Omarrrio
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories