What point on the graph of y = sin x is the closest to (0,1)?
Our topics include derivatives and optimization
Our topics include derivatives and optimization
2 Answers
Explanation:
We can find a distance function to the point via Pythagorean theorem:
We want to minimize
This equation is transcendental, i.e. we cannot actually solve it analytically. We have to solve numerically.
The plot of the above clearly only has one zero:
graph{x -cos(x)(1-sin(x)) [-3, 3, -3, 3]}
This is at
Explanation:
There's a nifty way to do this with any curve with a geometric property.
The line connecting (0,1) to (x, sin(x)) will have distance which peaks (is minimized) at a number
Perpendicular lines are negative inverses, i.e.
This must be solved numerically, not analytically. We find that