## anonymous 5 years ago Is sin 15 degrees is the same as pi/12? I'm suppose to find the exact value of the expression. multiple choice hw

1. amistre64

pi/3 = 60 pi/6 = 30 pi/12 = 15

2. amistre64

180/3 = 60 180/6 = 30 180/12 = 15

3. anonymous

so I got that part right. thanks! ......please continue explanation

4. anonymous

amistre amistre amistre

5. amistre64

sin(15) = sin(45-30)

6. anonymous

$\frac{\pi}{3}$ is not more 60 than 0 is 32

7. amistre64

sin(a-b) = sinacosb-sinbcosa

8. anonymous

0 degrees Celsius is the same temperature as 32 degrees F, but they are by no means the same number!

9. amistre64

pi 180 ---*---- = 60 3 pi

10. anonymous

true but that hardly means that $\pi = 180$ $\pi$ is a number close to 3, and 180 is many times bigger

11. amistre64

sin(15) = sin(45)cos(30) - sin(30)cos(45)

12. amistre64

when converting between degrees and radians; pi = 180

13. amistre64

just as 2pi = 360

14. anonymous

the point is that an angle measured is 15 degrees is the same as an angle measured in $\frac{\pi}{12}$ radians

15. anonymous

i will be quiet now

16. anonymous

mmm. i think i understand. is the exact value squareroot2 ( squareroot 3 - 1) over 4?

17. anonymous

thank you amistre and satellite! ..just please correct my answer if i'm wrong

18. amistre64

sin(15) = $$\frac{1}{\sqrt{2}}\frac{\sqrt{3}}{2}-\frac{1}{2}\frac{1}{\sqrt{2}}$$

19. amistre64

sin(15) = $$\frac{\sqrt{6}}{2}-\frac{\sqrt{2}}{2}$$

20. amistre64

over 4 is right

21. amistre64

$\sin(15)=\frac{\sqrt{6}-\sqrt{2}}{4}$ IF I DID IT RIGHT

22. amistre64

caps stuck lol

23. anonymous

nice latex too!

24. amistre64

i think i missed it somewhere

25. amistre64

$sin(15) = sin(45)cos(30) - sin(30)cos(45)$ ${\sqrt{2} \over 2}.{\sqrt{3}\over 2}-{1 \over 2}{\sqrt{2}\over 2}$ ${\sqrt{6}\over 4}-{\sqrt{2}\over4}$

26. anonymous

thank u i'm doing it on paper..ur much faster

27. amistre64

$\sqrt{6}-\sqrt{2} \over 4$

28. amistre64

this an take a few forms; all that equal the same thing but look different based upon how you went thru the stuff

29. amistre64
30. amistre64

im right lol

31. anonymous

WOW THANKS!