Question

How do you find an equation of the tangent line to the curve at the given point `y = 4 cos x` and `x=pi/6`?

Answer 1

Find `y', y'(pi/6) and y(pi/6)`, then find the equation of the line passes through `(pi/6, y(pi/6))` with the slope `m = y'(pi/6)`. Look the Explanation box below:

Explanation:

`y' = -4sin x`

`at x = pi/6:`

`y = 4cos (π/6)`
`y = 2sqrt 3`

`y' = -4sin (pi/6)`
`y' = -2`

`(pi/6, 2sqrt 3) and m = -2`
`y - 2sqrt 3 = -2(x - pi/6)`
`y = -2x + pi/3 +2sqrt 3`

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