### Introduction

In this Section we see how the equations of the tangent line and the normal line at a particular point on the curve $y=f\left(x\right)$ can be obtained. The equations of tangent and normal lines are often written as

$\phantom{\rule{2em}{0ex}}y=mx+c,\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}y=nx+d$

respectively. We shall show that the product of their gradients $m$ and $n$ is such that $mn$ is $-1$ which is the condition for perpendicularity.

#### Prerequisites

• be able to differentiate standard functions
• understand the geometrical interpretation of a derivative
• know the trigonometric expansions of $sin\left(A+B\right),\phantom{\rule{1em}{0ex}}cos\left(A+B\right)$

#### Learning Outcomes

• obtain the condition that two given lines are perpendicular
• obtain the equation of the tangent line to a curve
• obtain the equation of the normal line to a curve