# How do you find an equation of the tangent line to the curve at the given point y=sinx+3 and x=pi?

Jan 25, 2017

$y + x = 3 + \pi$

#### Explanation:

we use

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

where $\left({x}_{1} , {y}_{1}\right)$ is a known coordinate; and $m =$gradient

$y = \sin x + 3$

$y \left(\pi\right) = \sin \pi + 3 = 0 + 3 = 3$

$\left({x}_{1} , {y}_{1}\right) = \left(\pi , 3\right)$

gradient of tangent $m = {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}_{x = \pi}$

$y = \sin x + 3$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos x$

$m = {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}_{x = \pi} = \cos \pi = - 1$

eqn tgt

$y - 3 = - 1 \left(x - \pi\right)$

$y - 3 = - x + \pi$

$y + x = 3 + \pi$