Find the tangent line approximation T to the graph of f at the given point. f(x) = sin x, (8, sin 8)

Answer 1

f'(x) = cosx; slope of tangent line m = f'(8) = cos8.

Equation of tangent line: y - sin8 = (cos8)(x - 8); y = (cos8)x - 8cos8 + sin8;

So, T = (cos8)x - 8cos8 + sin8

Answer 2

We first need to find the slope of the line tangent to the graph, then using the given point, plug into the point-slope equation, y - y₁ = m(x - x₁), to find our equation of the line tangent to the graph at that point.

Slope = f'(x) so Slope = D_xsin(x) = cos(x).

Using the given point (8, sin(8)) we get:

y - sin(8) = cos(x)(x - 8)

y = (x)cos(x) - (8)cos(x) + sin(8)