Half angle formula?

Question

Alright, I'm studying for a test I have tomorrow and had a little question about the half angle formula.

In my textbook there is a section of questions with the directions: "Use the half-angle identities to find the exact values in problems 25-29"

the problems are as listed
25. cos^2(pi/3)
26. sin^2(pi/6)
27. sin^3(pi/6)
28. cos^2(pi/12)
29. sin^2(pi/8)

I know what the half angle formulas are (sin(x/2) = +/- sqrt((1-cosx)/2), etc. But I have trouble applying it. I don't know how to apply it regularly especially to numbers like pi/12 that don't have answers derived from the unit circle. I'm especially lost on what to do w/ the whole exponent in this set of questions. If someone can help me out, then I owe them. Thanks

Answer 1

I usually see the half angle formula written as :
sin^2 (x/2) = (1-cosx)/2

I don't know what they want you to do with 25 - 27 since you can easily answer those without using the half-angle identity.

For 28, rewrite it this way:
cos^2( (pi/6) /2 )
Now you can see that the x in the half angle formula is the same as pi/6 in your problem.

You can do the same thing for problems 28 and 29.
In problem 29 you'll have to use the identity twice. the first time will change pi/8 to pi/4. then you can use the identity again to change it to pi/2.

Answer 2

I would like to help you but it appears you are not aware that pi/2 is part of the unit circle--radians. There are 2 pi radians in a circle. pi/2 = 90 degrees, pi=180 degrees, pi/4 = 45 degrees, 2 pi = 360 degrees, etc.

Answer 3

the in basic terms trick is that u might want to wish to comprehend cos(a+b)=cosa*cosb+sina*sinb once you positioned a=b u get the double frame of mind formula in double frame of mind formula the signal for sin is useful between the formula and in a million/2 frame of mind it extremely is unfavourable once you do the derivations of formula you would possibly want to bear in recommendations it truthfully

Answer 4

25.cos^(pi/3)=3/4

26.sin^2(pi/6)=1/4

27.sin^3(pi/6)=1/8

28.cos^2(pi/12)=[(rt3 +1) / (2rt2)]^2

29.sin^2(pi/8)=