Sum and Difference Formulas

WARM-UP The expressions sin (A + B) and cos (A + B) occur frequently enough in math that it is necessary to find expressions equivalent to them that involve sines and cosines of single angles. So…. Does sin (A + B) = Sin A + Sin B Try letting  A = 30  and  B = 60 

11.3 Sum and Difference Formulas Objective: To use the sum and difference formulas for sine and cosine. sin (  +  ) = sin  cos  + sin  cos  sin (  -  ) = sin  cos  - sin  cos  1. This can be used to find the sin 105 . HOW? 2. Calculate the exact value of sin 375 . 30  60  45 

cos (  +  ) = cos  cos  - sin  sin  cos (  -  ) = cos  cos  + sin  sin  Note the similarities and differences to the sine properties. 3. This can be used to find the cos 285 . HOW? 4. Calculate the exact value of cos 345 .

Write each expression as the sine or cosine of a single angle. cos 80  cos 20  + sin80  sin 20   sin 30  cos 15  + sin15  cos30   cos 12  cos x  - sin12  sin x   Do you understand the difference between the sum and difference properties for sine and cosine difference? Assignment: ws 11.3

11.5a - Solving Trigonometric Equations Objective: To solve trigonometric equations involving special angles. What does it meant to solve over 0  < x < 360  ? What does it meant to solve over 0 < x < 2  ? Recall: You need the values of your special angles.  Do you have your unit circle?  Can you reproduce your special triangles?  Do you remember how to determine the values of your axis angles? 30  60  45 

Solve over the interval 0  < x < 360 . Solve over the interval 0 < x < 2 .