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anonymous

  • one year ago

If sin theta=3/5 and theta is in quadrant 2 determine in exact form sin theta+pi over 6

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  1. Loser66
    • one year ago
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    We have formula sin(a+b) = sin a *cos b + sin b *cos a your a = theta your b= pi/6 find cos theta, then plug all into it. |dw:1436465382393:dw|

  2. anonymous
    • one year ago
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    @Loser66 So I did all that and got the answer .9196 but I am off by a point when I check if it is right tho

  3. Loser66
    • one year ago
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    show your work, please

  4. anonymous
    • one year ago
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    Alright the end work I got 3sqrt3 over 10 + 2/5 but it doesn't come out correct -___-

  5. Loser66
    • one year ago
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    cos (theta) = 4/5 hence sin (theta + pi/6) = sin (theta) cos (pi/6) + sin (pi/6) cos (theta) = (3/5) (sqrt 3/2) + (1/2) (4/5) = 0.573

  6. anonymous
    • one year ago
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    But I still keep getting .919... answer ohmygod this is so frustarting lol @Loser66

  7. anonymous
    • one year ago
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    And when you go to check the answer it is suppose to be .90166

  8. freckles
    • one year ago
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    that is what it says when I punch in what loser has above

  9. freckles
    • one year ago
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    and 0.9196 is also what I'm getting

  10. freckles
    • one year ago
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    i think you are right @shortyyshayy

  11. freckles
    • one year ago
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    and they have an error

  12. anonymous
    • one year ago
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    @freckles Idk this is coming out weird cuz when checking it I am like a .1 off lol

  13. freckles
    • one year ago
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    just to be sure you are asked to evaluate \[\sin(\theta+\frac{\pi}{6})\]

  14. freckles
    • one year ago
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    well the other thing is it says it wants the EXACT form not an approximation

  15. freckles
    • one year ago
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    exact form would be \[\frac{2}{5}+\frac{3 \sqrt{3}}{10}\]

  16. freckles
    • one year ago
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    not .9196

  17. freckles
    • one year ago
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    which is just an approximation

  18. Loser66
    • one year ago
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    https://www.google.com/?gws_rd=ssl#q=online+calculator

  19. freckles
    • one year ago
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    omg I'm so dumb

  20. freckles
    • one year ago
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    I didn't see it said in quadrant 2

  21. freckles
    • one year ago
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    cos is negative there

  22. freckles
    • one year ago
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    \[\frac{3}{5} \frac{\sqrt{3}}{2}+\frac{-4}{5}\frac{1}{2}\]

  23. freckles
    • one year ago
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    which actually gives us .1196 so that still doesn't give us the answer you want

  24. Loser66
    • one year ago
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    yes!!! @freckles

  25. anonymous
    • one year ago
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    where did you get -4/5 from tho??

  26. freckles
    • one year ago
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    it says theta is in quadrant 2

  27. freckles
    • one year ago
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    cos is negative there and sin is positive there

  28. freckles
    • one year ago
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    sin(theta)=3/5 cos(theta) can be 4/5 or -4/5 depending on where theta is

  29. freckles
    • one year ago
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    and since cos is negative then cos(theta)=-4/5

  30. freckles
    • one year ago
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    here is another way to look at it we are given sin(theta)=3/5 \[\cos^2(\theta)+\sin^2(\theta)=1 \\ \cos^2(\theta)+(\frac{3}{5})^2=1 \\ \cos^2(\theta)+\frac{9}{25}=1 \\ \cos^2(\theta)=1-\frac{9}{25} \\ \cos^2(\theta)=\frac{25}{25}-\frac{9}{25} \\ \cos^2(\theta)=\frac{16}{25} \\ \cos(\theta)=\pm \sqrt{\frac{16}{25}} \\ \cos(\theta)=\pm \frac{4}{5}\]

  31. freckles
    • one year ago
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    now deciding whether to use 4/5 or -4/5 entirely depends on where theta is

  32. freckles
    • one year ago
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    |dw:1436467227803:dw|

  33. anonymous
    • one year ago
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    @freckles ohhh alright i think this is making more sense now! haha thanks so much!!!

  34. freckles
    • one year ago
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    |dw:1436467279746:dw|

  35. freckles
    • one year ago
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    hey so why are you looking for an approximation anyways?

  36. freckles
    • one year ago
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    you problem wants exact form

  37. anonymous
    • one year ago
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    I thought thats what it wanted in the first place lol

  38. freckles
    • one year ago
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    \[\frac{3}{5} \frac{\sqrt{3}}{2}+\frac{-4}{5}\frac{1}{2} \\ \frac{3 \sqrt{3}}{10}-\frac{2}{5}\] this is exact form

  39. freckles
    • one year ago
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    like the .1196 is an approximation to that exact form

  40. freckles
    • one year ago
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    .1196 is not exactly 3sqrt(3)/10-2/5 that is the funny thing about irrational numbers

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