## anonymous 5 years ago Help with trigonometry identities please! Simplify: a) cos(180º +x) + cos(180º - x) b) cos(7pi/126º)cos(36º/5)+sin(7pi/126º)sin(36º/5)

1. amistre64

cos(a+b) - cos(a-b): cos^2(a) - sin^2(a) + cos^2(a) + sin^2(a) 2cos^2(a) 2cos^2(180) ; cos(180) = -1 2(-1^2) = 2(1) = 2

2. amistre64

$7\pi/126^O$ ????

3. amistre64

if anything that would equal 7pi(180)/126pi ... but ive never seen anything written like that before.

4. anonymous

this is the equation:

5. amistre64

well, its a cos(a-b) construct, but i dunno about those digits

6. amistre64

if you convert the degrees to radians, then I spoose you can have a radian measure without a pi in it.... but its just unnatural :)

7. anonymous

ok..thanks for the help on the first one

8. amistre64

7pi = 180 degrees, lets substitute that in instead

9. amistre64

cos(180/126)cos(36/5) + sin(180/126º)sin(36/5)

10. amistre64

then cos(180/126 - 36/5) is your angle....

11. amistre64

add the fractions and simplify... right?

12. amistre64

3636 ----- 630

13. amistre64

602/105...whats our remainder?

14. anonymous

did u already multiply the fraction by cos? im confused, sorry :S

15. amistre64

5 + (77/105)

16. amistre64

you dont need to do that :) you just need to find the angle of the cos: cos(a - b); find a - b

17. amistre64

108(5) 36(126) ------ - -------- 126(5) 126(5)

18. amistre64

180(5) 36(126) ------ - -------- 126(5) 126(5) arghh!!..typoed it lol

19. amistre64

3636 cos of ----- is what I get 630

20. amistre64

-3636 ------ you gotta catch this stuff, cause I dont always ;) 630

21. anonymous

22. amistre64

that looked alot better in my head lol

23. amistre64

loco..... give me a sec; im on break ;)

24. anonymous

ok

25. anonymous

im not about to catch anything lol. i am very confused by trig in general..im about to post a question on trig identities...could u maybe help me through those when i post it? u seem like u know what ur doing :)

26. amistre64

its a farse, I no nutheeenng!!!

27. anonymous

he does. he know his stuff :)

28. anonymous

ur a superhero for a reason :)

29. amistre64

pfftt!!!.....super hero, now I gotta wear tights, and that aint a pretty picture ;)

30. amistre64

I get an angle of -5.77 degrees when we do all that.

31. amistre64

that is if its even right lol

32. amistre64

the cos of that angle = .9949 and thats the best I got fer ya on that one....right or wrong ;)

33. anonymous

r u solving the whole question btw? i just need to simplify..

34. amistre64

I solved it for the angle; andle = 5 + (77/105) and for the value of the cosine of that angle :=: .9949 how to simplify it is beyond me :)

35. anonymous

:'( ok. that's better than no answer at least!

36. amistre64

well, -5 and 77/105ths.... but yeah :) ..good luck with it; if anything, get it wrong and move ahead :)