Question

Find an equation of the tangent line to the curve at the given point? `y = sec(x) − 2 cos(x)`, `P = (π/3 , 1 )`

Answer 1

`y = 3sqrt3(x - pi/3)+1`

Explanation:

Given: `y = sec(x) − 2 cos(x), P = (π/3 , 1 )`

Compute the first derivative:

`dy/dx = 2sin(x) + tan(x)sec(x)`

The slope of the tangent line is the first derivative evaluated at the x coordinate of the point:

`m = 2sin(pi/3)+tan(pi/3)sec(pi/3)`

`m = 3sqrt3`

Use the point-slope form of the equation of a line:

`y = m(x-x_1)+y_1`

`y = 3sqrt3(x - pi/3)+1`