Calculus ( finding tangent to the curve question)

**Changhons** · June 10th 2009, 04:50 PM

Hi, I just can't do this question and i am not sure where i am getting it wrong.

4. Find the equation of the tangent to the curve x = cos ( 2y + pi) at (0, pi/4).

Give your answer in the form y= ax + b where a and b are constants to be found.

I have no idea how to get the gradient....

Please show your working.

Thanks a lot.

**TheEmptySet** · June 10th 2009, 04:56 PM

Originally Posted by Changhons

Hi, I just can't do this question and i am not sure where i am getting it wrong.

4. Find the equation of the tangent to the curve x = cos ( 2y + pi) at (0, pi/4).

Give your answer in the form y= ax + b where a and b are constants to be found.

I have no idea how to get the gradient....

Please show your working.

Thanks a lot.

Taking the derivative we get

$\frac{d}{dx} x =\frac{d}{dx}( cos(2y+\pi))$

$1=-\sin(2y+\pi)(2\frac{dy}{dx})$

Now we evaluate (0,pi/4) to get

$1=-2y' \sin\left( \frac{3\pi}{2}\right))$

$1=-2y'(-1) \iff y'=\frac{1}{2}$

I hope this helps

**HallsofIvy** · June 12th 2009, 02:52 AM

You could also just use m= dx/dy and write the equation of the line as $x= my+ \pi/4$ .

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