Question

For `f(x)=sinx` what is the equation of the tangent line at `x=(3pi)/2`?

Answer 1

`y = -1`

Explanation:

The equation of the tangent line of any function at `x = a` is given by the formula : `y = f'(a)(x-a) + f(a)`. So we need the derivative of `f`.

`f'(x) = cos(x)` and `cos((3pi)/2) = 0` so we know that the tangent line at `x = 3pi/2` is horizontal and is `y = sin((3pi)/2) = -1`