# How do you graph #theta=-840^circ#?

graph{-tan(2*pi/3)*x [-10, 10, -5, 5]}

First you simplify the angle so it's between 0 and 360º

So we have the equation

Since we only have an angle, the radius can be any real value, so our equation describes a line. Just find the appropriate angle on the graph paper and trace a line through it.

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To graph ( \theta = -840^\circ ), you would first convert the angle to its equivalent angle within one full revolution. Since ( 360^\circ ) represents one full revolution, adding or subtracting multiples of ( 360^\circ ) does not change the position of the angle on the graph.

To find the equivalent angle within one revolution, you would add or subtract multiples of ( 360^\circ ) until you obtain an angle between ( 0^\circ ) and ( 360^\circ ).

In this case, to find the equivalent angle:

[ -840^\circ + 360^\circ = -480^\circ ] [ -480^\circ + 360^\circ = -120^\circ ]

So, ( \theta = -840^\circ ) is equivalent to ( \theta = -120^\circ ) within one full revolution.

Now, to graph ( \theta = -120^\circ ), you would locate the angle ( -120^\circ ) on the unit circle or on a graph with polar coordinates. Since ( -120^\circ ) is measured clockwise from the positive x-axis, you would start from the positive x-axis and rotate clockwise by ( 120^\circ ). This places the point on the unit circle at ( (0.5, -\sqrt{3}/2) ).

Therefore, to graph ( \theta = -840^\circ ), you would graph the point ( (0.5, -\sqrt{3}/2) ).

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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.

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