Consider a circle with radius 10 that is centered at the origin. Find the exact x and y coordinates of the point on this circle corresponding to an -780 degrees.

Question

x = __________

y = __________

This question wants anyone to apply the exact answers by using square roots if necessary.

Answer 1

-780º = -720º - 60º

Now use 30-60-99 relationship to answer.

Answer 2

To find the x- and y- coordinates, you use the formula x = r cosθ and y = rsinθ, where r is the length of the radius and θ is the angle. Since the angle you are given is -780°, you can find a coterminal angle on the circle by adding multiples of 360°.

-780°+(360°)3 = 300°

So you have x = 10cos300° = 10 (1/2) = 5

and y = 10sin300° = 10 (√3/2) = 5√3.

Answer 3

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