## anonymous one year ago Find the exact value of each expression: a. sin20degcos80de-cos20degsin80deg b. cos 5pi/12cos7pi/12-sin5pi/12sin7pi/12

1. anonymous

@jim_thompson5910 does that make sense or should i write out again?

2. jim_thompson5910

you don't need to write "deg"

3. jim_thompson5910

hint: see page 2 of http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf specifically the "Sum and Difference Formulas" section

4. anonymous

so it would be the formula stating that sin(a +or-b)=sinacosb-cosasinb?

5. jim_thompson5910

correct

6. jim_thompson5910

you'll use the cosine version for part b

7. anonymous

oh okay so for the test tomorrow I should just memorize those formulas? but so now to solve it, it would be (20+80) or (20-80)? so the answer is 100 or -60?

8. jim_thompson5910

sin(20)cos(80)-cos(20)sin(80) = sin(20-80) = sin(-60) = ???

9. anonymous

oh wait oops

10. anonymous

would it be sin(60)?

11. anonymous

@jim_thompson5910

12. jim_thompson5910

sin(-60) is not equal to sin(60)

13. anonymous

oh .. i thought you put the question marks as in that it was wrong

14. jim_thompson5910

no it's my way of putting a blank

15. anonymous

it's pi/3

16. jim_thompson5910

so you'd fill in the blank

17. anonymous

ohh ok sorry

18. jim_thompson5910

sin(-60) = -sin(60) = _______________

19. anonymous

-pi/3

20. anonymous

@jim_thompson5910

21. jim_thompson5910

no not -pi/3

22. jim_thompson5910

you're thinking of -60 degrees = -pi/3 radians

23. jim_thompson5910

use the unit circle and determine -sin(60)

24. anonymous

okay i've been looking at the unit circle for 5 minutes and because you're determining -sin60 you would be looking in the 3 and fourth quadrants right?

25. anonymous

and looking for a distance of 60 degrees the opposite way? I'm just trying to remember what my teacher said.. He said something like that @jim_thompson5910

26. jim_thompson5910

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27. jim_thompson5910

|dw:1433398585790:dw|

28. jim_thompson5910

|dw:1433398602906:dw|

29. jim_thompson5910

determine the y coordinate of that point, then make it negative that will be the value of -sin(60)

30. anonymous

root 3/2?

31. jim_thompson5910

$\Large \sin(60) = \frac{\sqrt{3}}{2}$ $\Large -\sin(60) = -\frac{\sqrt{3}}{2}$

32. anonymous

okay so I just look for it on the unit circle and determine it through the coordinate?

33. jim_thompson5910

yes, x = cos(theta) and y = sin(theta)

34. anonymous

ok! got it!

35. anonymous

now for part b do you find pi/6 on the unit circle and look at x coordinate to determine the value?

36. anonymous

@jim_thompson5910