## lilsis76 Group Title 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 one year ago one year ago

1. dpaInc Group Title

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

2. lilsis76 Group Title

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?

3. lilsis76 Group Title

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

4. dpaInc Group Title

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

5. lilsis76 Group Title

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

6. lilsis76 Group Title

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

7. dpaInc Group Title

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

8. lilsis76 Group Title

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 ???

9. dpaInc Group Title

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)

10. dpaInc Group Title

are you familiar with the unit circle?

11. lilsis76 Group Title

yes, i had to memorize that thingy

12. dpaInc Group Title

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

13. lilsis76 Group Title

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

14. lilsis76 Group Title

ugh?! i do need h

15. dpaInc Group Title

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

16. lilsis76 Group Title

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

17. lilsis76 Group Title

30deg

18. dpaInc Group Title

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

19. lilsis76 Group Title

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

20. dpaInc Group Title

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

21. lilsis76 Group Title

$\sqrt{3}/2 , 1/2$

22. dpaInc Group Title

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

23. lilsis76 Group Title

okay, thank u, bye!

24. dpaInc Group Title

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