10-1 Formulas for cos(a+-B) and sin(a+-B)

This week I am going to explain how to work problems using formulas for cos(a+ or - B) and sin(a+ or - B). There are 6 different formulas for these types of problems. These formulas are:

1. cos(a + or - B)=cosa cosB - or + sina sinB
2. sin(a + or - B)=sina cosB + or - cosa sinB
3. sinx+siny=2sin (x+y/2) cos (x-y/2)
4. sinx-siny=2cos (x+y/2) sin (x-y/2)
5. cosx+cosy=2cos (x+y/2) cos (x-y/2)
6. cosx-cosy=-2sin (x+y/2) sin (x-y/2)

Now I am going to work some examples using these formulas. There are many different ways to work these problems.

Example 1: cos 105 degrees

• You are going to use your trig chart to help work this problem.
• You are going to use formula 1 to solve this problem.
• Since 45 and 60 degrees are on the trig chart and they add up to equal 105, you are going to use those two degrees.
• cos(45+60)=cos45 cos60-sin45 sin60
• You then plug those into the trig chart.
• You answer is going to be: square root of 2 - square root of 6/4

Example 2: sin75 cos15 + cos75 sin15

• You are going to replace this with one of your formulas above.
• That formula above is the same as sin(a+B)
• Once you replace with that formula you are going to get sin(75+15)=90 degrees
• sin 90 degrees on the trig chart equal 1
• 1 is goin to be your answer

And that is how you work problems using formuals for cos(a+B) and sin(a+B)

--Halie! :)