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Calc.

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Use a linear approximation (or differentials) to estimate the given number.

Tan 44 degrees

Please help.

  • Calc. - ,

    f(x)=tan(x)
    f'(x)=sec²(x)
    Using linear approximation:
    f(xo+δ)=f(xo)+δf'(xo) (approx.)

    Put xo=π/4 (in radians, = 45°)
    δ=π/180 (1°)
    f(44°)
    =f(xo-δ)
    =tan(π/4)-δ*sec²(π/4) (approx.)
    =1-π/180/cos²(π/4)
    =1-π/180/(1/2)
    =1-π/90
    =0.96509...

    accurate value of tan(44°)=0.96569...

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