These are the rest of my half of my notes on section 10.1. We will only be doing cos for this section.
The formula that you need to know for this part of the section is this:
cos (alpha+/- beta) = cosalphaxcosbeta -/+ sinalphasinbeta
Alpha and Beta can come from your trig chart. Remember that you need to add or subtract to get the angle that you are looking for.
First Equation
Find the exact value of cos 120 degrees.
cos ( 90+30)= cos 90 degrees x cos 30 degrees - sin 90 degrees x sin 30 degrees First, you need to figure out what angles in the trig chat equal 120 degrees and if you need to subtract or add to get to it. Since 90 degrees plus 30 degrees equals 120 degrees, you will use the subtraction formula for this equation. Then you simply fill out your formula with the information that you were given.
0 x square root of 3/2 + 1 x ½ Then you find out the trig functions by using your trig chart.
0 - 1/2 Then you multiply the 2 sides by themselves.
cos 120 degrees= -1/2 Finally you subtract them and you get this as your answer.
That is how you use the formula to find the exact value for cos.
Now lets learn how to simplify.
Simplify cos 30 degrees x cos 60 degrees + sin 30 degrees x sin 60 degrees.
cos 60 degrees x cos 30 degrees + sin 60 degrees x sin 30 degrees First, write out your equation.
cos ( 60 degrees- 30 degrees) Then, since you know that you’re using cos’s formula and subtraction thanks to the formula. You will put it like this.
cos 30 degrees Then you subtract the two degrees and you get this.
Square root of 3/2 Since 30degrees is on the trig chart you will use Square root of 3/2 as the answer to your question.
That is how you use the cos formula in these situations.
These are my notes on the rest of section 10.1.
SO UNTIL NEXT WEEK JA NE!!!
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