Find the Tangent Line at (2π,0) y=sin(sin(x)) , (2pi,0)

Problem

y=sin(sin(x)),(2*π,0)

Solution

1. Identify the function and the point of tangency. The function is y=sin(sin(x)) and the point is ((x_0),(y_0))=(2*π,0)

2. Differentiate the function using the chain rule to find the slope of the tangent line.

d(y)/d(x)=cos(sin(x))⋅cos(x)

3. Evaluate the derivative at x=2*π to find the slope m

m=cos(sin(2*π))⋅cos(2*π)

4. Simplify the trigonometric values. Since sin(2*π)=0 and cos(2*π)=1

m=cos(0)⋅1

m=1⋅1=1

5. Apply the point-slope formula y−(y_0)=m*(x−(x_0)) using m=1 and the point (2*π,0)

y−0=1*(x−2*π)

6. Solve for y to write the equation in slope-intercept form.

y=x−2*π

Final Answer

y=x−2*π

Want more problems? Check here!