10-1

10-1 Formulas for Cosine(α±β) and Sine(α±β)
So section 10-1 is about sine and cosine formulas used to simplify and find exact values of trigonometric functions. NO CALCULATORS ARE TO BE USED IN THIS SECTION. They will give you the wrong answer anyway. It is also necessary, better yet MANDATORY that you remember, memorize or what ever it is that that you need to to know the trig chart.
The formuals for sin and cos are as follows :
cos(α-β)= cosα cosβ + sinα sinβ
cos (α+β)= cosα cosβ - sinα sinβ

sine (α-β)= sin α cosβ – cosα sinβ
sine(α+β)= sin α cosβ + cosα sinβ

Notice, when using cosine, if the left side of the formula is using cos(α-β), then the right side or the formula is using addition and vice versa.

Some problems require you to simply simplify.
Ex.
Cos 105 cos 15 + sin 105 sin 15
Cos (α-β)
Cos (105-15)
Cos (90)
0


Other problems ask you to solve them, or “find exact value”.
Sin(105)
α= 45 β=60
sin ( 45+60)
= sin45 cos60 +cos45 sin60
=(sqrt2/2)(1/2)=(sqrt2/2)(sqrt3/2)
=sqrt2/4 + sqrt6/4
Sin 105 = sqrt2 + sqrt6/ 4

:)