Question

Use the half-angle formulas to come up with an exact expression for each formula value below. You do not have to simplify your answers.

a.) cos(pi/4)
b.)cos(pi/8)
c.)cos(pi/16)

Answer 1

How would you find this to simplify each one?

Answer 2

?? Why would you use a half-angle identity to find \(\cos(\pi/4) = \dfrac{\sqrt{2}}{2}\)?

Answer 3

Thats the question.... I'm trying to figure that out as well

Answer 4

I think the answer is supposed to be in degrees that is why

Answer 5

Well, I vote for skipping that one and starting with \(\pi/8\)

Since everything is in Quadrant I, let's just dive in.

We have the Double Angle Formula \(\cos(2x) = 2\cos^{2}(x) - 1\).

Demoting to Half Angle, we have:\(\cos(x) = 2\cos^{2}(x/2) - 1\).

Solving for the half angle gives: \(\cos(x/2) = \sqrt{\dfrac{\cos(x) + 1}{2}}\).

Using \(x = \pi/4\), we have: \(\cos(\pi/8) = \sqrt{\dfrac{\cos(\pi/4) + 1}{2}}\).

Wade through all that and then show me \(\cos(\pi/16)\)

Answer 6

Wouldn't it be the same thing but you would have the pi/16 numbers involved? because the decimal answer is .98

Answer 7

No decimals. "with an exact expression for " <== It's in the problem statement.

Put your calculator away!

Answer 8

Ok, but it says you don't have to simplify.. So I was right about the pi/16

Answer 9

Not if you think it should look like "0.98".

Maybe you could just rewrite my last expression with pi/16 on the outside and pi/8 on the inside? It's not perfectly clear what it means not to simplify.

Answer 10

Alright, Thank you!

Answer 11

@Ivlady you ok?