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lilsis76
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
yes.... it is that 4th formula..
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?
wait it would be the cos. right? ugh these formulas are confusing me
yes... the cosine one... just remember, the cosine formula (whether it's + or -), is cos * cos +/- sin * sin
okay, ill have to put that on a 3by5 card
okay! i think i got this just a second. let me know if its right or i made a mistake please.
so: \(\large cos(\frac{2\pi}{9}-\frac{\pi}{18})=cos(\frac{2\pi}{9})cos(\frac{\pi}{18})+sin(\frac{2\pi}{9})sin(\frac{\pi}{18}) \)
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 ???
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)
are you familiar with the unit circle?
yes, i had to memorize that thingy
wow... you seem like you don't need any help.... :)
so...my answer is going to be that unit?
so what's cos(pi/6) = ???
haha sorry about that. i just need help of steps walking through it, she went so fast in class. i only got pieces
yes... cos(pi/6) = cos(30 degrees) = ????
the points? is that what the ??? is for?
yes.... what's the x-coordinate ??? here is the unit circle...page 3 http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
i have to leave... sorry... the answer is cos(30 degrees) = \(\large \frac{\sqrt3}{2} \)
the x-coordinate refers to the cosine, the y-coordinate is sine. yw... :)