This week I'm going to review the sum and differences of sine and cosine. You will need the trig chart again in this chapter. Today I'm going to explain the sum and difference formulas of sine and cosine.They are:
1. cos(alpha+/-beta)=cos alpha cos beta-/+sin alpha sin beta
2. sin (alpha+/-beta)=sin alpha cos beta+/-cos alpha sin beta
3. sin x+sin y=2sinx+y/2 cos x-y/2
4. sin x-sin y=2cosx+y/c sin x-y/2
5. cos x+cos y=2cosx+y/2cosx-y/2
6. cos x-cos y=-2sinx+y/2 sin x-y/2
Now for an example.(REMEMBER: in this chapter you REPLACE, NOT PLUG IN!)1. cos(alpha+/-beta)=cos alpha cos beta-/+sin alpha sin beta
2. sin (alpha+/-beta)=sin alpha cos beta+/-cos alpha sin beta
3. sin x+sin y=2sinx+y/2 cos x-y/2
4. sin x-sin y=2cosx+y/c sin x-y/2
5. cos x+cos y=2cosx+y/2cosx-y/2
6. cos x-cos y=-2sinx+y/2 sin x-y/2
Find the exact value of Sin 15
1. Since sin 15 isn't on the trig chart, you must use a formula that will make it.
2. So you will use Sin(45-30)
3. You will now get, Sin45 cos 30-cos 45 sin30
4. Using the trig chart, you get Sqrt 2/2 x sqrt 3/2 - Sqrt 2/2 x sin 1/2
5. Simplify. You get (sqrt 6-sqrt 2)/4
And that's all there is to it (:
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