# Finding an equation tangent line

• Feb 21st 2013, 09:20 AM
homeylova223
Finding an equation tangent line
Hello everyone

How would i solve the following

Find an equation for the tangent line to the graph of x+sin(y-2x)=1 at the point (1,2)

I did

1+cos(y-2x)(dy/dx)(-2)=0

then I did cos(y-2x)(dy/dx)=2

(dy)/(dx)=(2)/(cos(y-2x) so would I just plug in the value of x and y.
• Feb 21st 2013, 10:27 AM
hollywood
Re: Finding an equation tangent line
That would give you the slope. You need the equation for the tangent line. The equation of a line through $\displaystyle (x_0,y_0)$ with slope m is $\displaystyle (y-y_0)=m(x-x_0)$.

- Hollywood
• Feb 21st 2013, 01:50 PM
HallsofIvy
Re: Finding an equation tangent line
Quote:

Originally Posted by homeylova223
Hello everyone

How would i solve the following

Find an equation for the tangent line to the graph of x+sin(y-2x)=1 at the point (1,2)

I did

1+cos(y-2x)(dy/dx)(-2)=0

then I did cos(y-2x)(dy/dx)=2

This is incorrect. from 1+ cos(y- 2x)(dy/dx)(-2)= 0 you get -2cos(y- 2x)(dy/dx)= -1 or cos(y- 2x)(dy/dx)= 1/2. When x= 1, y= 2, cos(2- 1)(dy/dx)= 1/2 so dy/dx= 1/cos(1).

Quote:

(dy)/(dx)=(2)/(cos(y-2x) so would I just plug in the value of x and y.
• Feb 21st 2013, 07:49 PM
MINOANMAN
Re: Finding an equation tangent line
the Gradient is 1 and the equation of the tangent is x-y=-1.
• Feb 21st 2013, 08:10 PM
ibdutt
Re: Finding an equation tangent line
There is a slight problem, when you differentiate you will get
1 + cos ( y - 2x ) [ dy/dx -2] = 0
At ( 1,2 ) we get dy/dx = 1
So the equation of tangent is ( y-2) = 1 * ( x-1)
OR
x - y + 1 = 0
• Feb 22nd 2013, 06:13 AM
hollywood
Re: Finding an equation tangent line
Yeah, $\displaystyle \frac{dy}{dx}=1$. Sorry I missed that.

- Hollywood