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March 11

Finding the tangent to a curve

Can someone please explain how the tangent triangle in this case [1] is constructed? Why does rotating it by 90 degrees do the trick? Thank you. Imagine Reason (talk) 00:26, 11 March 2018 (UTC)[reply]

It looks like x and y are in a 3:4 ratio. Then the tangent at point C is perpendicular to the line from the origin to point C, which has a slope of 4/3. The slope of the tangent line is the negation of the reciprocal of the slope of the line from the origin to C, so it is -3/4. Bubba73 ^{You talkin' to me?} 00:51, 11 March 2018 (UTC)[reply]

@Imagine Reason: In general, a tangent line is by definition perpendicular to a normal line. The hypotenuse of the triangle has the role of normal line first and then tangent line.--Jasper Deng (talk) 09:30, 11 March 2018 (UTC)[reply]

And the line from the origin to the curve is a normal line because this particular curve is a circle centered at the origin. That first step does not hold for arbitrary curves (though tangent line ⊥ normal line does). -- ToE 14:16, 11 March 2018 (UTC)[reply]