Question

What are the coordinates of the terminal point for 8 = 330°?

1
A.
-
I
22
1
V3
O B.
2
V3
1
O c.
2
D.
1 3
2 2

Answer 1

Explanation:

If you plot this angle in the coordinate plane, you will find yourself in the fourth quadrant with a referencew angle of 30. Constructing the triangle from that reference angle and using the Pythagorean triple for a 30-60-90 triangle, you get that the side adjacent to the reference angle is √3, the side opposite the reference angle is a -1, and the hypotenuse (which is NEVER negative!) is 2. The x and y coordinates of the terminal point result from the cos (related to the x coordinate) and the sin (related to the y coordinate). The cos of 30:

`cos(30)=(√(3) )/(2)` and the sin of 30:

`sin(30)=-(1)/(2)` so the coordinates of the terminal point on that angle are

`((√(3) )/(2),-(1)/(2))`

You could also just go to your unit circle, find the angle 330 and look at the coordiantes they give you there for (cos, sin). But I'm a high school math teacher so I wanted you to know how to find this outside of the unti circle. Cuz what if you lost it!?