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Identify a unit circle and describe its relationship to real numbers. Evaluate trigonometric functions using the unit circle. Use the domain and period to evaluate sine and cosine functions. Use a calculator to evaluate trigonometric functions. Why you should learn it.
Unit Circle Trigonometry Coordinates of Quadrantal Angles and First Quadrant Special Angles Based on the values of the sides of the triangle, we now know the coordinates of the point (, )x y where the terminal side of the 60o angle intersects the unit circle. This is the point ()1 3 22, , as shown below.
Practice Worksheet: The Unit Circle Fill in the blanks. 1. When a circle is divided into 8 equal sections, each central angle measures ___ __ __ degrees and ___ ____ radians. 2. All of the coordinates for special angles on the unit circle ca n be derived from the ___ ____ _ quadrant. 3. The angle whose terminal side passes through @ ¾ 7 6 á ? 5 6
The Unit Circle. We can form right-angled triangles in a unit circle (circle of radius 1). If θ is the anticlockwise angle between the positive x-axis and the ray −−→ OP then for all θ ∈ R: sinθ = y 1 = y , cosθ = x 1 = x and tanθ = y x. 1. x y x y. θ 1. O1. P(x,y) 1. x y x y. θ 1. O1. P(x,y) 1. y x y. θ 1 1. negative θ (clockwise) O P(x,y) 74.
The definition of a unit circle is: x2 + y2 =1 where the center is (0, 0) and the radius is 1. An angle of 1 radian is an angle at the center of a circle measured in the counterclockwise direction that subtends an arc length equal to 1 radius. Notice that the angle does not change with the radius.
Trigonometry and the Unit Circle. The following diagram shows a circle of radius 1 (this is called a unit circle). Point P is used to create a right-angled triangle. The coordinates of P are (x, y). -1. P (x, y) - 0 1. Level 1 – 2. Write down the length of the hypotenuse of the triangle.
Trigonometric Review Part 1. Defining the Functions. Recall, the graph of the equation 2 2 x y 1 is the unit circle. y. (x, y) = (cos , sin ) (1, 0) x. The Unit Circle. The graph of this equation is used to generate the trigonometric functions.
