This tells me I'm going to travel in quarters. The first location with a 2 in the denominator is π/2, a quarter of the circle away from 0. All I need to do is count around the circle until I get to 7.Ĥ. So I want to travel to all the places with a 2 in the denominator.ģ. If you didn't get that, here's how it works:Ģ. What you can get from this is that 0 and 2π are essentially the same thing with regard to the unit circle and will have the same values. So what would an equivalent value be for 7π/2? If you said 3π/2, you are correct! So we would think we would be at the location 2π, but the circle shows that location as 0. If we travel around another half of the circle, we have traveled π more in distance. For example, observe that if we travel from our starting point, 0 (the positive x-axis), and travel to π, we have traveled around half of the circle. In Quadrant IV, all cosine values will be positive, while sine values will be negative.Įquivalent Radian Measures of the Unit CircleĪs we 'travel' around the unit circle, the radian measures will continue to grow even though the circle only shows 0 through 11π/6. In Quadrant III, all cosine and sine values will be negative. So for Quadrant II, all cosine values will be negative and all sine values will be positive. The signs of the x- and y-coordinates will correspond with the location of the points in the quadrants. This process of placing special right triangles into quadrants of the unit circle can be repeated over and over to find coordinates for a 30°, 45°, and 60° angle in each quadrant. So when looking at the angle π/4, the corresponding unit circle point is (√2/2, √2/2).Īlso notice that a point on the unit circle is not only (x, y), but also (cos θ, sin θ), where θ is the measure of the angle in radians. We talk about angles of the unit circle always starting from the positive x-axis and rotating counterclockwise around the circle as shown with the green arrow above. Therefore, the measurements of the sides of the special right triangle become the coordinates of the point on the unit circle. Notice that the point on the unit circle, (x, y), corresponds with a width and height of a triangle.

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