Pre-Calc Exam Notes 71

Pre-Calc Exam Notes 71 - = A in Figure 3.2.1(a), and QPR =...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Sum and Difference Formulas Section 3.2 71 3.2 Sum and Difference Formulas We will now derive identities for the trigonometric functions of the sum and difference of two angles. For the sum of any two angles A and B , we have the addition formulas : sin ( A + B ) = sin A cos B + cos A sin B (3.12) cos ( A + B ) = cos A cos B sin A sin B (3.13) To prove these, ±rst assume that A and B are acute angles. Then A + B is either acute or obtuse, as in Figure 3.2.1. Note in both cases that QPR = A , since QPR = QPO OPM = (90 B ) (90 ( A + B ))
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = A in Figure 3.2.1(a), and QPR = QPO + OPM = (90 B ) + (90 (180 ( A + B ))) = A in Figure 3.2.1(b). B O Q N P M R A A A + B (a) A + B acute O Q N P M R A A A + B (b) A + B obtuse Figure 3.2.1 sin ( A + B ) and cos ( A + B ) for acute A and B Thus, sin ( A + B ) = MP OP = MR + RP OP = NQ + RP OP = NQ OP + RP OP = NQ OQ OQ OP + RP PQ PQ OP = sin A cos B + cos A sin B , (3.14)...
View Full Document

Ask a homework question - tutors are online