March 2 nd copyright2009merrydavidson HAPPY BIRTHDAY TO: Khalil Nanji.

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March 2 nd copyright2009merrydavidson HAPPY BIRTHDAY TO: Khalil Nanji

Sum and Difference Identities *You do NOT have to memorize these. * You do NOT get a calculator for these. *These identities are used for angles that are not “special”.

1) 2) 3) 4)

Ex 1: Find cos 15 Is 15 0 on the unit circle? Therefore we need to use the sum or difference identity. To find cos 15 we will use: cos (45 - 30)

Ex 1: Find cos 15 To find cos 15 we will use: cos (45 - 30) Step 1: write down the identity every time!

Ex 1: Find cos 15 Step 2: Fill in 45 and 30 for A and B (45 o is A; 30 o is B) cos (45 – 30) = cos 45 o cos 30 o + sin 45 o sin30 o

Ex 1: Find cos 15 Step 3: Using the unit circle, substitute the correct sine and cosine value into the formula. Keep things lined up! cos (45 – 30) = cos 45 o cos 30 o + sin 45 o sin30 o

Ex 1: Find cos 15 Step 4: Do the algebra. cos (45 – 30) = cos 45 o cos 30 o + sin 45 o sin30 o A better way to write this is:

Do #2 – 5 on your class worksheet now. Check your answers with mine as you go.

NEW TYPE OF PROBLEM HERE…. Ex 6: If sin = 5/13 and cos = 4/5 and  and  terminate in the same quadrant; find cos( + ) Step 1: Determine the quadrant using ASTC. Sine is positive in _____ and cosine is positive in _______ so draw the reference angles in ___. QI & II QI & IV QI

Ex 6: If sin = 5/13 and cos = 4/5 and  and  terminate in the same quadrant; find cos( + ) Sine is positive in _____ and cosine is positive in _______ so draw the reference angles in ___. QI & II QI & IV QI

Ex 6: If sin = 5/13 and cos = 4/5 and  and  terminate in the same quadrant; find cos( + ) Step 2: Label the reference triangles using the given information y x 4

Ex 6: If sin = 5/13 and cos = 4/5 and  and  terminate in the same quadrant; find cos( + ) Step 3: Use the pythagorean theorem to find x and y y x 4 y = 3 x = 12

Ex 6: If sin = 5/13 and cos = 4/5 and  and  terminate in the same quadrant; find cos( + ) Step 4: Use the “sum” identity to find the answer y = 3 x = 12

Ex 6: If sin = 5/13 and cos = 4/5 and  and  terminate in the same quadrant; find cos( + ) y = 3 x = 12

Do #7 on your worksheet now please. Keep things lined up.

Homework: WS 9-6