Start of Chapter Ten

In the first part of this chapter, 10-1, it involves sine and cosine formulas used to simplify and find exact values of trigonometric functions. No calculators are allowed to be used for this section. Well isn’t this just delightful. Anyway like I was saying, lesson 10-1 is showing us how to find the exact values and how to simplify trig functions. Alpha and beta come straight from your trig chart and +/- to get the angle you are looking for, no worries. All you pretty much need to know for this section is the trig chart and the two formulas below.

Cos(alpha +/- beta) = cos alpha cos beta -/+ sin alpha sin beta
Sin(alpha +/- beta) = sin alpha cos beta +/- cos alpha sin beta

Ex:
Find the exact value of sin 50 degrees.
1. There are two degrees from the trig chart that add up to equal 35, so those are the two numbers you will use. 45and 15
Alpha = 60
Beta = 45
2. Since it is asking for sin, you will use that formula.
Sin(60 + 45) = sin60 cos45 + cos60 sin45
3. You fill in everything on the right of the equal sign with the trig chart.
(square root 3/2)(square root 2/2) + (1/2)(square root 2/2)
4. Square root 6/4 + square root 2/4
5. The Final answer is square root 4 + square root 6/8.