Amy's Relfection #34 (Easter Blog)

okay now here is a review on some trig questions...
Example 1: Find the exact value of sin 80 cos 130+ cos 80 sin 130

Let alpha = 80 and beta = 130 then sin 80 cos 130 + cos 80sin 130 = sin alpha cos beta + cos alpha sin b

= sin (alpha + beta)
= sin (80+130)
= sin (210)
= sin (180 + 30)
= - sin 30
= -1/2

Example 2: Find the exact value of

cos^215 - sin^215 = cos(2alpha)
= cos(30)
= sqrt 3/2

Example 3: cos 15

alpha = 45, beta = 30

cos (alpha - beta) = cos 45 cos30 + sin45 sin 30

cos (45 - 30) = (√(2/2) (√(3/2) + (√(2/2) (1/2)

= √(√6 + √2)/all over 4

Example 4: (1 + cot^2) (1 - cos 2x)

(csc^2x) (1-cos2x)

(csc^2x) (1-(1 - 2sin^2x)

(1/sin^2x) (2sin^2x)

= 2

Example 4: Find the exact value of sin22.5

alpha=2(22.5)

alpha=45

**if you are given an angle with a decimal you use the half-angle formula. To find alpha, you multiply by two.

Example 5: Sum Formula for Cosine

cos 75 cos 15 + sin 75 sin 15

=cos (75-15) = cos 60 = 1/2

Example 6: Find the exact value of tan15 +tan30/1-tan15 (tan30)

= tan(15 + 30)

= tan(45)

=1

question time: can someone tell how to Rewriting a Sum or Difference as a Product??