# How do you find the equation of the tangent and normal line to the curve #y=tanx# at #x=-pi/4#?

##### 1 Answer

Nov 5, 2016

Tangent:

Normal:

#### Explanation:

The gradient tangent to a curve at any particular point is given by the derivative.

If

When

So the tangent passes through

Using

# y-(-1) = (2)(x-(-pi/4)) #

# :. y+1 = 2x+pi/2 #

# :. y = 2x+pi/2-1 #

The normal is perpendicular to the tangent, so the product of their gradients is -1 hence normal passes through

so the equation of the normal is:

# y-(-1) = -1/2(x-(-pi/4)) #

# :. y+1 = -1/2x-pi/2 #

# :. y = -1/2x-pi/8 -1 #