## apple_pi 2 years ago Simplify sin^2(54)+cos^2(72)

1. apple_pi

Please don't just go sin 54 = blah and cos(72) = blah, so blah + blah = blahblah

2. apple_pi

@Callisto

3. tukajo

is 54 the actual number or is that in 54 degrees?

4. apple_pi

54 degrees

5. zzr0ck3r

So you just want to know how to computte this by hand?

6. apple_pi

yes

7. apple_pi

why did you go into radians?

8. apple_pi

so what is x equal to?

9. tukajo

I fluttered that up ignore me.

10. tukajo

11. Callisto

\[sin^2(54)+cos^2(72)\]\[=(cos(90-54))^2+cos^2(72)\]\[=cos^2(36)+cos^2(72)\] That looks nicer

12. apple_pi

Oh, wait... let me try now

13. Callisto

Okay :|

14. apple_pi

cos^2(36) + (2cos^2(36)-1)^2

15. apple_pi

am i right?

16. Callisto

Yes.

17. apple_pi

now... do we evaluate cos(36) or simplify more?

18. Callisto

Evaluate.

19. apple_pi

ok. is this straightforward or something we fancily work out?

20. Callisto

very fancy :|

21. Callisto

let x = 36 5x = 180 3x = 180 - 2x sin 3x = sin2x 3 sinx - 4sin^3 x = 2sinx cox Since sinx =/= 0 3- 4 sin^2 x = 2cosx 3- 4 ( 1-cos^2 x) = 2 cos x 4 cos^2 x - 2cosx -1 =0 Now, solve for cosx.

22. zzr0ck3r

wow

23. Callisto

@apple_pi Come back :'(

24. zzr0ck3r

So in what class do we learn to play with this trick?

25. Callisto

I'm sorry, I don't know. I'm not from the US. But for me, I learnt it two years before university.

26. apple_pi

Sorry... I had to go for a while

27. apple_pi

Yeah that solved it! Thanks @Callisto

28. Callisto

You're welcome. FYI, this post is worth looking! http://openstudy.com/study#/updates/4fe6e718e4b02c91101b52cd

29. apple_pi