# What is the equation of the tangent line of #r=2cos(theta-pi/2) + sin(2theta-pi)# at #theta=pi/4#?

form is

Here,

The slope of the tangent at P is

So, the equation to the tangent is

form is

graph{(sqrt(x^2+y^2)(x^2+y^2-2y)+2xy)(0.877x-0.48y-0.116)((x-.293)^2+(y-.293)^2-.009)=0 [-5, 5, -2.5, 2.5]}

The Cartesian form is used for the Socratic graph.

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To find the equation of the tangent line of ( r = 2\cos(\theta - \frac{\pi}{2}) + \sin(2\theta - \pi) ) at ( \theta = \frac{\pi}{4} ), first, express the polar equation in terms of Cartesian coordinates. Then, find the derivative ( \frac{dy}{dx} ) with respect to ( \theta ). Finally, use the point-slope form of a line equation to find the equation of the tangent line.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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