# Find the Tangent Line at the Point y=sin(sin(x)) , (4pi,0)

,
Find and evaluate at and to find the slope of the tangent line at and .
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
The derivative of with respect to is .
Replace all occurrences of with .
The derivative of with respect to is .
Reorder the factors of .
Reform the equation by setting the left side equal to the right side.
Replace with .
Evaluate at and .
Replace the variable with in the expression.
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
The exact value of is .
Plug in the slope of the tangent line and the and values of the point into the pointslope formula .
Simplify.
The slope-intercept form is , where is the slope and is the y-intercept.
Rewrite in slope-intercept form.
Subtract from .
Simplify .
Multiply by .
Multiply by .
Find the Tangent Line at the Point y=sin(sin(x)) , (4pi,0)