# What is the equation of the line that is normal to the polar curve #f(theta)=sin(2theta+pi) -theta# at #theta = pi/4#?

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To find the equation of the line normal to the polar curve (f(\theta) = \sin(2\theta + \pi) - \theta) at (\theta = \frac{\pi}{4}), we first need to find the slope of the tangent to the curve at that point.

Differentiate (f(\theta)) with respect to (\theta) to find (f'(\theta)). Then, evaluate (f'(\frac{\pi}{4})) to get the slope of the tangent line.

The slope of the normal line will be the negative reciprocal of the slope of the tangent line.

Once you have the slope of the normal line and the point ((\theta, f(\theta))) where it passes through, you can use the point-slope form of the equation of a line to find the equation of the normal line.

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