10-3

In 10-3, like all the other lessons in chapter 10, there is a good bit of formulas.

1. sin2(alpha) = 2sin(alpha)cos(beta)
2. cos2(alpha) = cos^2(alpha)-sin^2(alpha)
3. cos2(alpha) = 1-2sin^2(alpha)
4. cos2(alpha) = 2cos^2(alpha)-1
5. tan2(alpha) = 2tan(alpha)/1-tan^2(alpha)
6.sin(alpha)/2 = +or- square root of 1-cos(alpha)/2
7. cos(alpha)/2 = +or- square root of 1+cos(alpha)/2
8. tan(alpha)/2 = +or- square root of 1-cos(alpha)/1+cos(alpha)
9. tan(alpha)/2 = sin(alpha)/1+cos(alpha)
10. tan(alpha)/2 = 1-cos(alpha)/sin(alpha)

Eample 1: Simplify the given expression
2cos^2 10degrees-1

So you look at your formulas to see which one you could use. You can use formula 4 and all you have to do is replace the alphas with 10 degrees.
cos(2(10)) = cos 20 degrees, this is not on the trig chart so you can not simplify it anymore.

Example 2: Simplify the given expression
2sin(alpha)/2cos(alpha)/2

You would use the 1st formula for this. sin2(alpha/2). The 2's cancel and you get sin(alpha)

Example 3: Find the exact value of each expression
2cos^2 3(alpha)-1

You use the 4th formula. cos2(3alpha) = cos6(alpha). That is your final answers

Example 4: Find the exact value of each expression
2tan(pi/8)/1-tan^2(pi/8)

You use the 5th formula. tan2(pi/8). You cange that to degrees pi/8 is 45/2 so when you simplify tht you get tan45 which when you look on the trig chart is 1

---Danielle :)