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## lilsis76 3 years ago 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.

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1. zepdrix

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

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

3. zepdrix

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

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

5. lilsis76

okay.

6. lilsis76

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

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

8. lilsis76

what does that mean?

9. zepdrix

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

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

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

12. lilsis76

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

13. lilsis76

squ rt 3 /2

14. lilsis76

okay hold on lol

15. zepdrix

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

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

17. zepdrix

k good good c: Now simplyyyyyyyyyy \:D/

18. lilsis76

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

19. lilsis76

i get sqrt3 /2 - 1/2

20. zepdrix

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

21. lilsis76

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

22. zepdrix

Water you talking about? D:

23. lilsis76

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

24. zepdrix

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

25. lilsis76

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

26. zepdrix

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

27. lilsis76

okay then, thank you for helping me :D

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