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What is the polar form of the point with coordinates (4, 3π/4) and −9−9i √3?

User Soundmaven
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1 Answer

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Final answer:

The polar form of the point with coordinates (4, 3π/4) is (√(16 + 9π^2/16), arctan((3π/4)/4)).

Step-by-step explanation:

The polar form of a point with Cartesian coordinates (x, y) can be represented as (r, θ), where r is the distance from the origin to the point and θ is the angle the line connecting the origin and the point makes with the positive x-axis.

To find the polar form of the point (4, 3π/4), we first need to find the distance from the origin using the Pythagorean theorem:

r = √(x^2 + y^2) = √(4^2 + (3π/4)^2)

r = √(16 + 9π^2/16)

The angle θ can be found using the inverse tangent function:

θ = arctan(y/x) = arctan((3π/4)/4)

Therefore, the polar form of the point (4, 3π/4) is (√(16 + 9π^2/16), arctan((3π/4)/4)).

User Miroslav Popovic
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