# What is the slope of the tangent line of #r=3sin(theta/2-pi/4)# at #theta=(3pi)/8#?

Slope at

Relating this to Cartesian coordinates, we know that

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To find the slope of the tangent line of the polar curve ( r = 3 \sin(\frac{\theta}{2} - \frac{\pi}{4}) ) at ( \theta = \frac{3\pi}{8} ), you need to take the derivative of ( r ) with respect to ( \theta ) and evaluate it at ( \theta = \frac{3\pi}{8} ). Then, use the formula for the slope of a tangent line in polar coordinates, which is given by ( \frac{dr}{d\theta} + r\frac{d\theta}{dr} ).

After finding the derivative of ( r ) with respect to ( \theta ) and evaluating it at ( \theta = \frac{3\pi}{8} ), and similarly, finding ( \frac{d\theta}{dr} ) and evaluating it at the same point, you can plug the values into the formula for the slope of the tangent line to get the final answer.

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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.

- How do you find the slope of the polar curve #r=1+sin(theta)# at #theta=pi/4# ?
- What is the distance between the following polar coordinates?: # (4,(7pi)/4), (3,(3pi)/8) #
- How do you find the equation of the tangent lines to the polar curve #r=sin(2theta)# at #theta=2pi# ?
- How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3(1-costheta)#?
- What is the polar form of #(1,3)#?

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