# What is the Cartesian form of #(12,(-7pi)/3))#?

It can be seen from the diagram that the x coordinate of P is

So:

From example:

Cartesian coordinate:

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

The Cartesian form of the point ( (12, -\frac{7\pi}{3}) ) is ( (12, -\frac{7\pi}{3}) ). However, if you meant to convert the point from polar coordinates to Cartesian coordinates, the process is as follows:

Given the point ( (r, \theta) = (12, -\frac{7\pi}{3}) ), where ( r ) is the distance from the origin and ( \theta ) is the angle in radians measured counterclockwise from the positive x-axis, we can use the formulas:

[ x = r \cos(\theta) ] [ y = r \sin(\theta) ]

Substituting the given values:

[ x = 12 \cos\left(-\frac{7\pi}{3}\right) ] [ y = 12 \sin\left(-\frac{7\pi}{3}\right) ]

Now, simplify:

[ x = 12 \cos\left(-\frac{2\pi}{3}\right) ] [ y = 12 \sin\left(-\frac{2\pi}{3}\right) ]

[ x = 12 \left(-\frac{1}{2}\right) ] [ y = 12 \left(-\frac{\sqrt{3}}{2}\right) ]

[ x = -6 ] [ y = -6\sqrt{3} ]

So, the Cartesian form of ( (12, -\frac{7\pi}{3}) ) is ( (-6, -6\sqrt{3}) ).

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

- What is the equation of the tangent line of #r=theta-sin(-theta+(pi)/3) # at #theta=(2pi)/3#?
- What is the slope of the polar curve #f(theta) = theta^2 - sec^3theta+tantheta # at #theta = (3pi)/4#?
- What is the slope of the polar curve #f(theta) = theta - sec^3theta+thetasin^3theta # at #theta = (5pi)/8#?
- What is the Cartesian form of #( 8 , (13pi)/6 ) #?
- What is the Cartesian form of #(12,(-7pi)/3))#?

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