lilsis76 3 years ago 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

1. dpaInc

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

2. lilsis76

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

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

4. dpaInc

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

5. lilsis76

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

6. lilsis76

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

7. dpaInc

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

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

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

are you familiar with the unit circle?

11. lilsis76

yes, i had to memorize that thingy

12. dpaInc

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

13. lilsis76

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

14. lilsis76

ugh?! i do need h

15. dpaInc

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

16. lilsis76

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

30deg

18. dpaInc

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

19. lilsis76

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

20. dpaInc

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

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

22. dpaInc

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

23. lilsis76

okay, thank u, bye!

24. dpaInc

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