How do you find the polar coordinates for (-1, -4*π/3)?

#(-1,-4π/3)

1 Answer
Perihelion
Mar 18, 2018

#(4, 77°)# (Both values to 1.dp)

Explanation:

To solve this question you must imagine a triangle that has a base distance of #-1# and a height of #-4*π/3#.

We want to do this so that we can find out how far and at what angle the polar coordinates are and so that we can convert the current cartesian coordinates #(x,y)# to the polar coordinates #(r,θ)#.

The triangle

Base#=x = -1#
Height#=y=-4*π/3#
Hypotenuse#=r#
The angle between #r# and #x = θ#

Use Pythagoras Theorem to find the hypotenuse (#r#)

#r=sqrt((-1)^2+(-4*π/3)^2)#

#r=sqrt(16.54596338)=4.067672969#

#r = 4# (1d.p)

Use the Tangent Function to find the desired angle

#tan(θ)=(-4*π/3)/-1#

#θ = tan^-1((-4*π/3)/-1)=76.57295824#

#θ = 77°# (1d.p)

#:.# the Cartesian Coordinates #(-1,-4*π/3)# are #(4, 77°)# in Polar Coordinates.

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