Ch 5.4: Sum and Difference Formulas Learn these!! sin ( u + v ) = sin u cos v + cos u sin v sin ( u − v ) = sin u cos v − cos u sin v cos ( u + v ) = cos u cos v − sin u sin v cos ( u − v ) = cos u cos v + sin u sin v tan u + tan v tan ( u + v ) = 1 − tan u tan v tan u − tan v tan ( u − v ) = 1 + tan u tan v sin(u ± v) tan ( u ± v ) = cos(u ± v) How do we use this? Finding exact values of trig expressions 1. Split the given number into the sum/difference of unit circle values we know 2. Change the problem using the correct formula 3. Simplify by replacing in trig values Examples: Find the exact values Ex : cos ( 75 o ) cos ( 30o + 45o ) 1. Split 75o into 30o and 45o since π π o o 30 = 6 and 45 = 2. Use the cosine formula cos ( 30o ) cos ( 450 ) − sin ( 30o ) sin ( 450 ) 3 2 1 2 i − i 2 2 2 2 6 2 − = 4 4 4 3. Replace with Trig values ⎛ 3 1⎞ ⎛ 2 2⎞ o 30 = ⎜⎜ , ⎟⎟ and 45 = ⎜⎜ , ⎟⎟ ⎝ 2 2⎠ ⎝ 2 2 ⎠ o 6− 2 4