Question

using addition formulas for sine and cosine to simplify the expression:

cos (2pi/9) cos (pi/18) + sin (2pi/9) sin(pi/18)

I want to learn it the normal way first before I add my instructors instructions to place S=45 & T = 30.

here are the formulas given:

sin(s+t) = sin s cos t + cos s sine t
sin(s-t) = sin s cos t - cos s sine t
cos(s+t) = cos s cos t - sin s sin t
cos(s-t) = cos s cos t + sin s sin t

The they way it looks, it seems to use formula 4:
cos(s-t) = cos s cos t + sin s sin t

Answer 1

yes.... it is that 4th formula..

Answer 2

YAY! okay
um... i know that know would i fill it in like this...
well wait, first I have a question, how can i find out if its cos or sin that im looking for?

Answer 3

wait it would be the cos. right? ugh these formulas are confusing me

Answer 4

yes... the cosine one...
just remember, the cosine formula (whether it's + or -), is cos * cos +/- sin * sin

Answer 5

okay, ill have to put that on a 3by5 card

Answer 6

okay! i think i got this just a second. let me know if its right or i made a mistake please.

Answer 7

so:
\(\large cos(\frac{2\pi}{9}-\frac{\pi}{18})=cos(\frac{2\pi}{9})cos(\frac{\pi}{18})+sin(\frac{2\pi}{9})sin(\frac{\pi}{18}) \)

Answer 8

Cos(2pi/9 – pi/18)
mult. 2 to the left side……. So
cos(4pi/18-pi/18) I guess giving me…….cos 3pi/18?
Or do I simplify to get the cos pi/6 ???

Answer 9

now...
\(\large \frac{2\pi}{9}-\frac{\pi}{18}=\frac{4\pi}{18}-\frac{\pi}{18}=\frac{3\pi}{18}=\frac{\pi}{6} \)
that expression actually is cos(pi/6)

Answer 10

are you familiar with the unit circle?

Answer 11

yes, i had to memorize that thingy

Answer 12

wow... you seem like you don't need any help.... :)

Answer 13

so...my answer is going to be that unit?

Answer 14

ugh?! i do need h

Answer 15

so what's cos(pi/6) = ???

Answer 16

haha sorry about that. i just need help of steps walking through it, she went so fast in class. i only got pieces

Answer 17

30deg

Answer 18

yes... cos(pi/6) = cos(30 degrees) = ????

Answer 19

the points? is that what the ??? is for?

Answer 20

yes....
what's the x-coordinate ???
here is the unit circle...page 3
http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Answer 21

\[\sqrt{3}/2 , 1/2\]

Answer 22

i have to leave... sorry...
the answer is cos(30 degrees) = \(\large \frac{\sqrt3}{2} \)

Answer 23

okay, thank u, bye!

Answer 24

the x-coordinate refers to the cosine, the y-coordinate is sine.
yw... :)