# What is the slope of the tangent line of #r=(2theta+sin2theta)/cos^2theta# at #theta=(-3pi)/8#?

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

To find the slope of the tangent line at a specific point on a polar curve, you can use the formula: ( \frac{dr}{d\theta} = \frac{dy}{dx} = \frac{r' \sin(\theta) + r \cos(\theta)}{r' \cos(\theta) - r \sin(\theta)} ) where (r') represents ( \frac{dr}{d\theta} ).

First, calculate (r') by finding ( \frac{dr}{d\theta} ). Then plug the given value of (\theta) into the equation to find the slope of the tangent line.

Given ( r = \frac{2\theta + \sin(2\theta)}{\cos^2(\theta)} ), take the derivative ( r' = \frac{dr}{d\theta} ).

( r' = \frac{d}{d\theta}\left(\frac{2\theta + \sin(2\theta)}{\cos^2(\theta)}\right) )

After differentiation, evaluate (r') at ( \theta = \frac{-3\pi}{8} ).

This will give you the slope of the tangent line at the given point.

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.

- How do you use polar coordinates to evaluate the integral which gives the area that lies in the first quadrant between the circles #x^2+y^2=36# and #x^2-6x+y^2=0#?
- What is the distance between the following polar coordinates?: # (21,(4pi)/3), (11,(11pi)/8) #
- What is the equation of the line that is normal to the polar curve #f(theta)= cos(pi-2theta)+thetasin(5theta-pi/2) # at #theta = pi/2#?
- Consider the system? −3x + 5y + 3z = 0 6x + −7y + −4z = −2 9x + −6y + −3z = −6 Gaussian elimination of the augmented matrix for this system produces the matrix
- What is the distance between the following polar coordinates?: # (3,(-4pi)/3), (4,(-5pi)/6) #

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