math

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

Please explain ^_^

asked by jojo
  1. so we want
    tanx = sinx
    sinx/cosx = sinx
    cosx = 1
    x = 0º, 360º, 720º, ...
    As you can see there is no such "largest" angle, they agree (are equal ?) at every multiple of 360º

    BTW, then value of the "agreement" would be 0,
    i.e. sin360=0, tan360=0
    sin 720 = 0, tan 720 = 0 etc.

    posted by Reiny
  2. The answer is indefinite, since both tangent and sin are cyclic functions.

    If we look for the largest angle between 0 and 2π, then we set
    sin(x)-tan(x) = 0.005 (for two significant digits)
    Solving for x, we get
    x=1.931688π=6.06858 radians
    Check: sin(x) = -0.2129628
    tan(x) = -0.2179628
    Thus sin(x) and tan(x) agree within 2 significant figures.

    posted by MathMate
  3. If you had to put the answer in radians what would it be?

    posted by jojo
  4. mmmhhh, looks like MathMate and I took a different interpretation.

    I think I read is as if there had been a comma after 'agree', ie

    Find the largest angle for which sine and tangent agree, to within two significant figures.

    posted by Reiny
  5. I think that is how the question is suppose to be interpreted Reiny. Very confusing wording.

    posted by jojo
  6. I guess we should use the first derivative to see the max

    posted by Engineer R

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