Cos(a +/- B) and sin(a +/- B)

Things you need to know:

• cos(a +/- B) = cosa(cosB) -/+ sina(sinB)
• sin(a +/- B) = sina(cosB) +/- cosa(sinB)
• 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)

Example 1: Find the exact value of cos75 degrees.

• You will first go to your trig chart to find out what adds to give you 75 for cos.
• Those numbers are 45 and 30.
• You are going to use those numbers in the first formula from above.
• cos(45 + 30) = cos45(cos30) - sin45(sin45)
• Now you plug in what those are from the trig chart.
• (square root of 2/2)(square root of 3/2) - (1/2)(square root of 2/2)
• square root of 6/4 - square root of 2/4
• Final answer: square root of 6 - square root of 2/4

Example 2: sin30(cos15) + cos30(sin15)

• For this problem they give you the two numbers they are adding so you have to replace it with one of the formulas.
• If you look at the problem and the formulas you have from above, it is the same as sin(a + B).
• Now you can replace.
• sin(30 + 15) = sin(45)
• Now that you have gotten an answer, you have to see what sin(45) is on the trig chart.
• sin(45) on the trig chart is square root of 2/2.
• Final answer: square root of 2/2.

-Amber :)