## keelyjm Group Title Help finding exact values. one year ago one year ago

1. keelyjm Group Title

Find an exact value. sin 75°

2. keelyjm Group Title

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

3. ZeHanz Group Title

How did you do it?

4. ZeHanz Group Title

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

5. keelyjm Group Title

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 Group Title

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

7. keelyjm Group Title

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 Group Title

I am not familiar with that equation.

9. ZeHanz Group Title

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 Group Title

yes to find the final answer.

11. ZeHanz Group Title

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

12. keelyjm Group Title

I have a pic in front of me that I drew

13. keelyjm Group Title

14. phi Group Title

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

15. phi Group Title

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

16. keelyjm Group Title

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

17. phi Group Title

I (for one) switch to degrees first.

18. keelyjm Group Title

how do I do that?

19. phi Group Title

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 Group Title

|dw:1360100026509:dw|

21. keelyjm Group Title

So I would do sin(45-30)

22. mariomintchev Group Title

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

23. keelyjm Group Title

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

24. phi Group Title

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

25. keelyjm Group Title

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 Group Title

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 Group Title

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

28. keelyjm Group Title

Oh I wrote it wrong and forgot to negate it

29. phi Group Title

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 Group Title

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

31. ZeHanz Group Title

@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 Group Title

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 Group Title

and basically I figured out how to use the equation

34. ZeHanz Group Title

Good for you!