10-1

This was a very tough week for me studying for exams, so I am glad we only learned one new lesson. We started 10-1 on Friday. The worst part about it is that we are not allowed to use calculators. The purpose of this section is to find exact values and to simplify. In order to do this section, you MUST know your trig chart. There are only two formulas to remember:

Cos(alpha +/- beta) = cosalpha cosbeta -/+ sinalpha sinbeta
Sin(alpha +/- beta) = sinalpha cosbeta +/- cosalpha sinbeta

Alpha and Beta come straight out of the trig chart.

Ex:
Find the exact value of sin 105 degrees.

1. There are two degrees from the trig chart that add up to equal 105, so those are the two numbers you will use. 60 and 45
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 6 + square root 2/4