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ASAPT

  • one year ago

Find a possible solution to the equation sin (3x+13)=cos(4x)

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  1. ASAPT
    • one year ago
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    @LegendarySadist

  2. ASAPT
    • one year ago
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    its part of my geometry course @LegendarySadist trig is one of the sections lol

  3. ASAPT
    • one year ago
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    @misssunshinexxoxo @ybarrap

  4. ASAPT
    • one year ago
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    nah at my schools it goes algebra 1 geometry algebra 3 and pre calc or discrete math im in geometry summer school

  5. ASAPT
    • one year ago
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    *algebra 2

  6. freckles
    • one year ago
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    use a co-function identity

  7. freckles
    • one year ago
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    for example, recall one of the co-function identities is: \[\cos(u)=\sin(\frac{\pi}{2}-u)\]

  8. ASAPT
    • one year ago
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    wow that really confused me

  9. freckles
    • one year ago
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    why does it confuse you?

  10. ASAPT
    • one year ago
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    because this stuff is like another language to me

  11. freckles
    • one year ago
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    but why does the identity confuse you?

  12. freckles
    • one year ago
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    is it because you never seen it?

  13. ASAPT
    • one year ago
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    kinda this is my first time learning this

  14. freckles
    • one year ago
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    |dw:1436410191044:dw|

  15. freckles
    • one year ago
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    could you find cos(theta) and sin(90-theta) using this right triangle ?

  16. freckles
    • one year ago
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    |dw:1436410266489:dw|

  17. freckles
    • one year ago
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    \[\sin(90-\theta)=\frac{v}{c} \text{ and } \cos(\theta)=\frac{v}{c} \\ \text{ that means } \sin(90-\theta)=\cos(\theta) \\ \] of course this is all true if we are working in degress

  18. freckles
    • one year ago
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    since I used 90 deg there

  19. freckles
    • one year ago
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    but we can do the same thing for radians and say \[\sin(\frac{\pi}{2}-\theta)=\cos(\theta)\]

  20. ASAPT
    • one year ago
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    would the answer be 13?

  21. freckles
    • one year ago
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    \[\sin(3x+13)=\cos(4x) \\ \text{ by cofunction identity you have that you can find a solution from } \\ \text{ setting the insides of this thingy equal } \\ \sin(3x+13)=\sin(\frac{\pi}{2}-4x)\]

  22. ASAPT
    • one year ago
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    so what would that make the answer be?

  23. freckles
    • one year ago
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    set the insides equal

  24. freckles
    • one year ago
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    and solve for x

  25. freckles
    • one year ago
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    \[3x+13=\frac{\pi}{2}-4x \]

  26. ASAPT
    • one year ago
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    I still don't get my answer

  27. freckles
    • one year ago
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    to solve a linear equation first you do: you put all your x terms on one side and your non-x terms on the opposing side by adding and subtracting stuff on both sides

  28. ASAPT
    • one year ago
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    oh so its 11

  29. freckles
    • one year ago
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    your answer should have pi in it somewhere so 11 isn't the answer

  30. freckles
    • one year ago
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    or a answer in this case

  31. freckles
    • one year ago
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    In general to solve the linear equations of the form ax+b=cx+d you do: \[ax+b=cx+d \\ \text{ subtract} cx \text{ on both sides } ax-cx+b=cx-cx+d \\ \text{ now } ax-cx=(a-c)x \text{ and } cx-cx=0 \\ \text{ so we have } (a-c)x+b=0+d \\ \text{ now subtract } b \text{ on both sides } (a-c)x+b-b=d-b \\ (a-c)x+0=d-b \\ (a-c)x=d-b \\ \text{ now final step is to divide }(a-c) \text{ on both sides } \\ \text{ so we have } x=\frac{d-b}{a-c}\]

  32. ASAPT
    • one year ago
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    the options are 11 -13 13 and 0

  33. freckles
    • one year ago
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    oh then you didn't have to find a possible solution using any identities just plug in those numbers to see which gives you the same thing on both sides

  34. ASAPT
    • one year ago
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    so what would the answer come out to be

  35. freckles
    • one year ago
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    have you tried pluggin in the choices as I suggested above?

  36. ASAPT
    • one year ago
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    i only have 1 minute until i have to submit it

  37. freckles
    • one year ago
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    I think they mean all of that to be in degrees so put your calculator on degrees and see which of the following is true: \[\sin(3(0^o)+13^o)=\cos(4(0^o) ) \\ \sin(3(11^o)+13^o)=\cos(4(11^o)) \\ \sin(3(13^o)+13^o)=\cos(4(13^o)) \\ \sin(3(-13^o)+13^o)=\cos(4(-13^o))\]

  38. freckles
    • one year ago
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    you can definitely rule out the first since we know sin(13 deg) isn't cos(0 deg) then check the second equation with 11 degs and so on... until you have the same thing on both sides

  39. freckles
    • one year ago
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    what is sin(3*11 deg+13 deg)=?

  40. freckles
    • one year ago
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    give you a hint 3*11+13=33+13=46 and guess what 90-46 is?

  41. freckles
    • one year ago
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    recall the above you can do this part without calculator come on you know sin(x)=cos(90-x) so sin(46)=cos( ? )

  42. freckles
    • one year ago
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    also it would be helpful in the future if you say if we are working in deg or radians because I thought it was radians until I seen your choices

  43. freckles
    • one year ago
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    good luck

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