Math

Find the largest angle for which sine and tangent agree to within two significant figures. Express your answer using two significant figures.

Answer in radians

?_?

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asked by Anya
  1. Please help, I have to turn this in soon and I keep on getting the wrong answer.
    I keep on getting .27 radians.

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    posted by Anya
  2. please

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    posted by Anya
  3. You need to show some working; I get 0.24.

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    posted by Dr Russ
  4. Can you show how you got 0.27?
    Also, it appears that yourself or jojo has asked the same question a few days ago. You could check the related post and answers at:
    http://www.jiskha.com/display.cgi?id=1251499014

    It should be stressed that since both sine and tangents are cyclic functions, the "largest" angle has to be bounded, such as 0 to 2π, or 0 to π/2, etc.
    I got 0.2146 by solving the equation
    tan(x)-sin(x)=0.005

    The way you solve the equation will depend on what course you are taking, it could be by tabulation, trial and error, Newton's method, or series expansions.
    This is probably why Dr. Russ would like to see your work.

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    posted by MathMate
  5. I got .27 through trial and error. I haven't learned how to do trig equations which stinks and this is for physics. How did you get .24 Dr Russ?

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    posted by Anya
  6. Ok, lets use iteration. You got .27 radians.
    I will use my calc to determine the values..
    Tan(.27)-sin(.27)=.0100266 which is too high, so reduce the angle to .20
    tan(.20)-sin(.20)=.00404 too low, so increase the angle
    tan(.25)-sin(.25)=.0079, too high, reduce it again... (you could guess here, but my knowing the small angle approximation..)
    tan(.22)-sin(.22)=.0054
    slightly high, still, so once more..
    tan(.215)-sin(.215)=.005027 getting close. I would take .215 rad as the answer.

    So what I have done is just do iteration (up when the result is too low, down when too high). YOu don't have to know much trig to do this. You do need a good calculator.

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