Question

What is the equation of the tangent line of `f(x)=sinpix-cospix` at `x=3`?

Answer 1

`f(x)=1-pi(x-3)`

Explanation:

`f'(x)=picospix+pisinpix`

Slope at x=3:
`f'(3)=picos3pi+pisin3pi=-pi+0=-pi`

Point:
`f(3)=sin3pi-cos3pi=0-(-1)=1;(3,1)`

Equation:
`f(x)=f(a)+f'(a)(x-a)`
`f(x)=1-pi(x-3)`