10-1

So this week I am going to help you refresh your memory on problems using two different formulas. This is really easy! There are only two formulas that you need to you learn. These formulas are:

• cos (a +/- B) = cos a cos B -/+ sin a sin B
• sin (a +/- B) = sin a cos B +/- cos a sin B

Those are the two main formulas although they are some others you may need to know.

• sinx + siny=2sin(x+y/2) cos(x-y/2)
• sinx - siny=2cos(x+y/2) sin(x-y/2)
• cosx + cosy=2cos(x+y/2) cos(x-y/2)
• cosx - cosy=-2sin(x+y/2) sin(x-y/2)

Okay, so now that I gave you the formulas I am going to do a few examples for yall so yall can better understand how to work these problems.

Example 1: Find the exact value of sin 150 degrees

• Look at the trig chart to see if any of the degrees add or subtract to equal 150. Which is 90+60=150
• So you then plug it in the sin formula given above.
• You will then get Sin(90+60)=Sin90Cos60+Cos90Sin60
• After that you plug it all into the trig chart and get your exact value answer.
• And its that easy!

Example 2: Solve for sin75 cos15 + cos75 sin15

• All you do for this one is plug it into the formula that matches it from above.
• Which is sin(alpha + beta)= sin (alpha) cos (beta) + cos (alpha) sin (beta)
• You then should get sin(75+15)= sin 90 = 1 for your answer.

And that is it for this weeek. Have a happy new years!

-Halie