# Find the Tangent Line at the Point y=sin(sin(x)) , (3pi,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 .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
The exact value of is .
Multiply by .
Subtract full rotations of until the angle is greater than or equal to and less than .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
The exact value of is .
Multiply by .
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 .
Apply the distributive property.
Simplify the expression.
Rewrite as .
Multiply by .
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