Find the equation of the tangent line to y=sinx at x=2pie

y = x - 2π

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)  

x₁ - x coordinate y₁ - y coordinate m - slope

Pre-Calculus

Unit Circle

Calculus

The definition of a derivative is the slope of the tangent line.

Derivatives of Trig Functions

sin(x) = cos(x)cos(x) = -sin(x)tan(x) = sec²(x)sec(x) = sec(x)tan(x)csc(x) = -csc(x)cot(x)cot(x) = -csc²(x)

Step-by-step explanation:

Step 1: Define

y = sinx

x = 2π

Step 2: Find Derivative

Take derivative:                   y' = cosx

This is the function of the tangent line for y.

Step 3: Find slope

Substitute in x into y':                    y'(2π) = cos2πEvaluate:                                        y'(2π) = 1

This tells us that the slope of the tangent line is 1 at x = 2π.

Step 4: Write equation

Find a point.

Substitute x into y:                     y(2π) = sin2πEvaluate:                                    y(2π) = 0Write coordinate:                      (2π, 0)

Write tangent function.

Substitute:                    y - 0 = 1(x - 2π)Simplify:                        y = x - 2π

This is the equation of the tangent line at x = 2π.

B. 2 1/2 feet. multiply 2.5 inches by 12 to get thirty inches then divide by 12 to get 2.5 feet