# What is the distance between the following polar coordinates?: # (1,pi/3), (-1,pi/2) #

These are both on the unit circle.

Since

The point

So, the point

Using the distance formula :

distance

hope that helped

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

The distance between the polar coordinates ( (r_1, \theta_1) ) and ( (r_2, \theta_2) ) is given by the formula:

[ d = \sqrt{r_1^2 + r_2^2 - 2r_1r_2\cos(\theta_2 - \theta_1)} ]

For the given polar coordinates ( (1, \frac{\pi}{3}) ) and ( (-1, \frac{\pi}{2}) ), the distance is:

[ d = \sqrt{1^2 + (-1)^2 - 2(1)(-1)\cos\left(\frac{\pi}{2} - \frac{\pi}{3}\right)} ]

Simplifying:

[ d = \sqrt{1 + 1 - 2(-1)\cos\left(\frac{\pi}{6}\right)} ] [ d = \sqrt{2 + 2\cos\left(\frac{\pi}{6}\right)} ] [ d = \sqrt{2 + \sqrt{3}} ]

So, the distance between the polar coordinates ( (1, \frac{\pi}{3}) ) and ( (-1, \frac{\pi}{2}) ) is ( \sqrt{2 + \sqrt{3}} ).

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 arclength of the polar curve #f(theta) = sin(3theta)-4cot6theta # over #theta in [0,pi/4] #?
- How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3costheta#?
- What is the distance between the following polar coordinates?: # (2,(12pi)/8), (1,(-pi)/8) #
- What is the polar form of #( 36,48 )#?
- What is the polar form of #( -4,-2 )#?

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