Answer:
y = x - 2π
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
Point-Slope Form: y - y₁ = m(x - x₁)
<u>Pre-Calculus</u>
<u>Calculus</u>
The definition of a derivative is <em>the slope of the tangent line</em>.
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:
<u>Step 1: Define</u>
y = sinx
x = 2π
<u>Step 2: Find Derivative</u>
- Take derivative: y' = cosx
This is the function of the tangent line for y.
<u>Step 3: Find slope</u>
- Substitute in <em>x</em> into y': y'(2π) = cos2π
- Evaluate: y'(2π) = 1
This tells us that the slope of the tangent line is 1 at x = 2π.
<u>Step 4: Write equation</u>
<em>Find a point.</em>
- Substitute x into y: y(2π) = sin2π
- Evaluate: y(2π) = 0
- Write coordinate: (2π, 0)
<em>Write tangent function.</em>
- Substitute: y - 0 = 1(x - 2π)
- Simplify: y = x - 2π
This is the equation of the tangent line at x = 2π.