## keelyjm 2 years ago Help finding exact values.

1. keelyjm

Find an exact value. sin 75°

2. keelyjm

$\frac{ \sqrt{6}+\sqrt{2} }{ 4 }$ Is this right?

3. ZeHanz

How did you do it?

4. ZeHanz

It is right, but what kind of help are you looking for?

5. keelyjm

I do not know how to do it, but looking at a unit circle that seemed correct with where the angle should be. I want to know what equatin to use to get that answer for future use.

6. ZeHanz

Do you know the formula: sin(a+b)=sin(a)cos(b)+cos(a)sin(b)?

7. keelyjm

Like currently I am stuck on Find an exact value. sine of negative eleven pi divided by twelve.$\sin(-\frac{ 11\pi }{ 12 })$

8. keelyjm

I am not familiar with that equation.

9. ZeHanz

OK, that makes it a lot more difficult, I guess. sin(-11pi/12)=-sin(11pi/12)=-sin(pi/12)=-sin(15°) Have you been instructed to do these kind of problems in a unit circle?

10. keelyjm

yes to find the final answer.

11. ZeHanz

OK, I'll try to draw one...

12. keelyjm

I have a pic in front of me that I drew

13. keelyjm

14. phi

I think you try to use "nice numbers" that add or subtract to get 75º 45º + 30º = 75º

15. phi

now use sin(a+b)= sin(a)cos(b) + cos(a) sin(b)

16. keelyjm

I already figured that one out. I am working on$\sin(-\frac{ 11\pi }{ 12 })$

17. phi

I (for one) switch to degrees first.

18. keelyjm

how do I do that?

19. phi

multiply by 180/pi you get -165 degrees that means go clockwise from the x-axis. as a positive angle it is 360-165= 195 degrees so you want to find the sin(15) in the 3rd quadrant

20. phi

|dw:1360100026509:dw|

21. keelyjm

So I would do sin(45-30)

22. mariomintchev

phi, when you're done here, can you come back to my problem? thanks!

23. keelyjm

so would I do sin(45)cos(30)-cos(45)sin(30) next?

24. phi

yes, but remember that sin is negative in the 3rd quadrant so minus the final answer

25. keelyjm

So how would I do that? I am thinking the answer would be $\frac{ -\sqrt{6}-\sqrt{2} }{ 4 }$ Just from what I know so far and the unit circle.

26. phi

sin(45)cos(30)-cos(45)sin(30) should give you $\frac{ \sqrt{6}-\sqrt{2} }{ 4 }$ now negate it to get $\frac{ \sqrt{2}-\sqrt{6} }{ 4 }$

27. phi

you can always check your answers using a calculator. sin(-165º) = -0.2588...

28. keelyjm

Oh I wrote it wrong and forgot to negate it

29. phi

so to do these problems, figure out the "reference angle" (that is the angle less than 90 that you make with the x-axis) and what quadrant. try to come up with sums or differences that give the reference angle and then use the formulas finally, use the quadrant to assign the correct sign.

30. keelyjm

Alright I will have to write that down. Thank you.

31. ZeHanz

@keelyjm: I thought you weren't familiar with sin(a+b)=sin(a)cos(b)+cos(a)sin(b)? Now you are using it... Glad you do, because it makes everything much easier ;)

32. keelyjm

Yeah after I saw that with unusual angles you had to split it into to normal angles I got where a and b went

33. keelyjm

and basically I figured out how to use the equation

34. ZeHanz

Good for you!