How do you convert x 2 to polar form?

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How do you convert x 2 to polar form?

1 Answer

  1. POLAR→CARTESIAN. You can see that from Pythagoras: r=√x2+y2 and from Trigonometry: θ=arctan(yx) .
  2. CARTESIAN→POLAR. From rigonometry: x=rcos(θ) y=rsin(θ)
  3. Let us consider our expression: x=2. let us use our second transformation formulas in the form: x=rcos(θ) to get: rcos(θ)=2. and: r=2cos(θ)

What is polar form of an equation?

The polar form of a complex number z=a+bi is z=r(cosθ+isinθ) . So, first find the absolute value of r . Now find the argument θ . Since a>0 , use the formula θ=tan−1(ba) .

How do you convert rectangular to polar form?

To convert from Cartesian coordinates to polar coordinates: r=√x2+y2 .

What is Y x in polar form?

The polar form is rsin(θ)=rcos(θ) . The points of the line y = x are given by r = 0 and sin(θ)=cos(θ) or, instead, θ=π4andθ=−3π4 .

What is the polar form of 2?

2(cosπ+isinπ)

How do you solve for polar coordinates?

How to: Given polar coordinates, convert to rectangular coordinates.

  1. Given the polar coordinate (r,θ), write x=rcosθ and y=rsinθ.
  2. Evaluate cosθ and sinθ.
  3. Multiply cosθ by r to find the x-coordinate of the rectangular form.
  4. Multiply sinθ by r to find the y-coordinate of the rectangular form.
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How do you add complex numbers in polar form?

To add complex numbers in rectangular form, add the real components and add the imaginary components. Subtraction is similar. To multiply complex numbers in polar form, multiply the magnitudes and add the angles. To divide, divide the magnitudes and subtract one angle from the other.

What is the formula for polar form?

Since a > 0 , use the formula θ = tan − 1 ( b a ) . θ = tan − 1 ( 2 5 ) ≈ 0.38. Note that here θ is measured in radians. Therefore, the polar form of 5 + 2 i is about 5.39 ( cos ( 0.38 ) + i sin ( 0.38 ) ) .

What is the polar form of complex numbers?

The polar form of a complex number is a different way to represent a complex number apart from rectangular form. Usually, we represent the complex numbers, in the form of z = x+iy where ‘i’ the imaginary number. But in polar form, the complex numbers are represented as the combination of modulus and argument.

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What is polar and rectangular form?

Both polar and rectangular forms of notation for a complex number can be related graphically in the form of a right triangle, with the hypotenuse representing the vector itself (polar form: hypotenuse length = magnitude; angle with respect to horizontal side = angle), the horizontal side representing the rectangular “real” component, and the