Question

Use the formula cos(s+t)=cos s cos t - sin s sin t:
to compute the exact value of cos 75 degrees.

all i know is that 75 degrees is between 90 deg and 60 degrees on a unit circle.

Answer 1

Hmmmmm we have special angles for 30, 45, 60, 90... do any of those 2 add up to 75? Cause that would really help us out in this problem.

Answer 2

well... okay we have the 30 and 45 angles

Answer 3

Hmm good good :) I think we can work with that.
So we'll rewrite cos(75) as cos(45+30).
After we apply the sum formula, we should be able to plug in a BUNCH of special angles and HOPEFULLY we'll be able to simplify it :3 hehe

Answer 4

So use your formula you posted at the top, what will your setup look like? :D

Answer 5

okay.

Answer 6

the 45 will be the s, and t will be tht 30 so...
cos(s+t)=cos s cos t - sin s sin t:
cos(45+30)= cos 45 cos 30 - sin 45 sin 30.
yes??

Answer 7

Mmmmmmmmmmmmmm yah looks good.
Now it's special angle time! :OOO

Answer 8

what does that mean?

Answer 9

Let's look at the first ..thing.. cos(45), what is the cosine of 45 degrees? It's a special angle that you're suppose to remember.. (from the unit circle) :X

Answer 10

OH....so the points are the special angles??? I thought that meant another formula to remember. um... 45 is at squ rt. 2 / squ rt. 2 / 2
cos sin
cos is squ.rt. 2 / 2

Answer 11

so cos(45)=sqrt2/2
and cos(30)? :D
Go through all of them and do yer magic!

Answer 12

what?! the 30 ? um... hold on

Answer 13

squ rt 3 /2

Answer 14

okay hold on lol

Answer 15

so our first term cos(45)cos(30) becomes..
(sqrt2/2)(sqrt3/2) Which we should be able to simplify a little bit. hmm

Answer 16

okay tis..
(sqrt2 /2)( sqrt3/2) - (sqrt 2/2)(1/2)

Answer 17

k good good c:

Now simplyyyyyyyyyy \:D/

Answer 18

uh...hold on let me try doin it um..

Answer 19

i get sqrt3 /2 - 1/2

Answer 20

Hmmmm this is what I'm coming up with D: