## lilsis76 Group Title Use the formula cos(s+t)=cos s cos t - sin s sin t: to compute the exact value of cos 75 degrees. all i know is that 75 degrees is between 90 deg and 60 degrees on a unit circle. one year ago one year ago

1. zepdrix Group Title

Hmmmmm we have special angles for 30, 45, 60, 90... do any of those 2 add up to 75? Cause that would really help us out in this problem.

2. lilsis76 Group Title

well... okay we have the 30 and 45 angles

3. zepdrix Group Title

Hmm good good :) I think we can work with that. So we'll rewrite cos(75) as cos(45+30). After we apply the sum formula, we should be able to plug in a BUNCH of special angles and HOPEFULLY we'll be able to simplify it :3 hehe

4. zepdrix Group Title

So use your formula you posted at the top, what will your setup look like? :D

5. lilsis76 Group Title

okay.

6. lilsis76 Group Title

the 45 will be the s, and t will be tht 30 so... cos(s+t)=cos s cos t - sin s sin t: cos(45+30)= cos 45 cos 30 - sin 45 sin 30. yes??

7. zepdrix Group Title

Mmmmmmmmmmmmmm yah looks good. Now it's special angle time! :OOO

8. lilsis76 Group Title

what does that mean?

9. zepdrix Group Title

Let's look at the first ..thing.. cos(45), what is the cosine of 45 degrees? It's a special angle that you're suppose to remember.. (from the unit circle) :X

10. lilsis76 Group Title

OH....so the points are the special angles??? I thought that meant another formula to remember. um... 45 is at squ rt. 2 / squ rt. 2 / 2 cos sin cos is squ.rt. 2 / 2

11. zepdrix Group Title

so cos(45)=sqrt2/2 and cos(30)? :D Go through all of them and do yer magic!

12. lilsis76 Group Title

what?! the 30 ? um... hold on

13. lilsis76 Group Title

squ rt 3 /2

14. lilsis76 Group Title

okay hold on lol

15. zepdrix Group Title

so our first term cos(45)cos(30) becomes.. (sqrt2/2)(sqrt3/2) Which we should be able to simplify a little bit. hmm

16. lilsis76 Group Title

okay tis.. (sqrt2 /2)( sqrt3/2) - (sqrt 2/2)(1/2)

17. zepdrix Group Title

k good good c: Now simplyyyyyyyyyy \:D/

18. lilsis76 Group Title

uh...hold on let me try doin it um..

19. lilsis76 Group Title

i get sqrt3 /2 - 1/2

20. zepdrix Group Title

|dw:1350602295589:dw| Hmmmm this is what I'm coming up with D:

21. lilsis76 Group Title

okay, but wouldn't it be - sqrt 4 /2?

22. zepdrix Group Title

23. lilsis76 Group Title

like okay, wouldnt the sqrt 6 / 4 - sqrt2/4 be a sqrt 4/4 leading to 2/4=1/2 ?

24. zepdrix Group Title

No you can't subtract those sqrt's like that :c you have to leave them alone.

25. lilsis76 Group Title

okay, so next time i get sq roots like that, just leave it alone?

26. zepdrix Group Title

Yah that is a good place to stop c: $\frac{ \sqrt6 -\sqrt2 }{ 4 }$

27. lilsis76 Group Title

okay then, thank you for helping me :D