Maths(difference)
2007-10-02 2:44 pm
Find the equations of the tangent lines to the graph of f(x) = sinx at x =0 and at x = pie / 3. Use each tangent line to approximate sin(pie/6). Would you expect these results to be equally accurate, since they are taken equally far away from x = pie/6 but on opposite sides? If the accuracy is different, can you account for the difference?
回答 (1)
2007-10-02 4:34 pm
✔ 最佳答案
Since f'(x) = cos xwhen x = 0,
f(0) = sin 0 = 0,
f'(0) = cos 0 = 1
equation : y - 0 = 1(x - 0)
i.e. y = x
when x = π/ 3 ,
f(π/ 3) = sin (π/ 3) = √3 / 2,
f'(π/ 3) = cos(π/ 3) = 1 / 2
equation : y - √3 / 2 = (1 / 2)(x - π/ 3)
i.e. 3x - 6y + 3√3 - π= 0
when x = π/ 6 ,
f(π/ 6) = sin (π/ 6) = 1 / 2,
f'(π/ 6) = cos(π/ 6) = √3 / 2
equation : y - 1 / 2 = (√3 / 2)(x - π/ 6)
i.e. 6√3x - 12y + 6 - √3 = 0
Obviously, the accuracy is different
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