SOLUTION: Of the infinitely many lines that are tangent to the curve of y = -sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope

Question 958546: Of the infinitely many lines that are tangent to the curve of y = -sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

A line tangent to the curve at point has a slope of .
Since it goes through point (,) and the origin then the slope also equals.

So then,

So to find the root, let

Then,

Now using Newton's method with a starting value of

.
So then at , the slope is equal to,

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