Chapter 10 was all about formulas. These are the formulas from chapter 10 section 1. Note: the trig chart will be needed as well throughout the entire chapter. The formulas are very specific and must be followed accordingly. If one memorizes these formulas, the chapter becomes fairly easy.
Formulas
cos(alpha +/-beta)=cos alpha cos beta-/+sin alpha sin betaFormulas
sin x+sin y=2sinx+y/2 cos x-y/2cos x-cos y=-2sinx+y/2 sin x-y/2
All you have to do is REPLACE the angle measures with the numbers from the trig chart.
Ex: 1 Find the exact value of Sin 75
1. sin 75 is not on the trig chart, so a formula must be picked for use
2. So one will use Sin(45+30)
3. When expanded, it looks like 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. Now all that is left is simplifying the answer.It comes out to be
sin (alpha+/-beta)=sin alpha cos beta+/-cos alpha sin beta
sin x-sin y=2cosx+y/c sin x-y/2
cos x+cos y=2cosx+y/2cosx-y/2
All you have to do is REPLACE the angle measures with the numbers from the trig chart.
Ex: 1 Find the exact value of Sin 75
1. sin 75 is not on the trig chart, so a formula must be picked for use
2. So one will use Sin(45+30)
3. When expanded, it looks like 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. Now all that is left is simplifying the answer.It comes out to be
(sqrt 6+sqrt 2)/4
-Sameer
-Sameer
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