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현재 위치

Equation of a straight line (tangential line) tangent to a trigonometric function

작성자 Uploader : chocopi 작성일 Upload Date: 2019-03-10변경일 Update Date: 2019-03-12조회수 View : 306

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For a point (x1, y1) on a trigonometric function y = a*x^3 + b*x^2 + c*x + d, the equation of a straight line tangent to this point P (x1, y1) can be obtained as follows.

From the trigonometric equation, the coordinates of the point P are (x1, a*x1^3 + b*x1^2 + c*x1 + d).

Assuming that the equation of tangential line is y = a1*x + b1,

The slope a1 of the tangential line at point P is :

a1 = 3*a*x1^2 + 2*b*x1 + c

Further, since it passes the point P, b1 can be obtained as follows.

a*x1^3 + b*x1^2 + c*x1 + d = (3*a*x1^2 + 2*b*x1 + c)*x1 + b1

b1 = (a*x1^3 + b*x1^2 + c*x1 + d) - (3*a*x1^2 + 2*b*x1 + c)*x1

▶ Input data

■ y coordinate of the tangent point (x1, y1)

■ slope at the tangent point (x1, y1)

■ y-intercept of the tangential line

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1st Step for All

현재 위치

Equation of a straight line (tangential line) tangent to a trigonometric function

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