# What is the slope of the polar curve #f(theta) = theta^2 - sectheta # at #theta = (3pi)/4#?

The slope:

From the reference Tangents with Polar Coordinates we obtain the equation

Substitute this into equation [2]:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the slope of the polar curve ( f(\theta) = \theta^2 - \sec(\theta) ) at ( \theta = \frac{3\pi}{4} ), you need to find the derivative of the function with respect to ( \theta ) and then evaluate it at ( \theta = \frac{3\pi}{4} ).

The derivative of the given function is:

[ \frac{df}{d\theta} = 2\theta - \sec(\theta)\tan(\theta) ]

Evaluating this derivative at ( \theta = \frac{3\pi}{4} ), we get:

[ \frac{df}{d\theta}\Bigg|_{\theta=\frac{3\pi}{4}} = 2\left(\frac{3\pi}{4}\right) - \sec\left(\frac{3\pi}{4}\right)\tan\left(\frac{3\pi}{4}\right) ]

Simplify this expression to find the slope of the polar curve at ( \theta = \frac{3\pi}{4} ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- What is the area under the polar curve #f(theta) = theta^2-thetasin(7theta-pi/6 ) +cos(2theta-(5pi)/4)# over #[pi/8,pi/2]#?
- What is the polar form of #(4,-2)#?
- What is the distance between the following polar coordinates?: # (3,(3pi)/4), (2,(7pi)/8) #
- How do you evaluate #log_216 6#?
- What is the distance between the following polar coordinates?: # (5,(-5pi)/12), (5,(11pi)/6) #

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7