7.3 Trig. Functions on the Unit Circle. 7.3 CONT. T RIG F UNCTIONS ON THE U NIT C IRCLE Objectives:  Graph an angle from a special triangle  Evaluate.

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Presentation transcript:

7.3 Trig. Functions on the Unit Circle

7.3 CONT. T RIG F UNCTIONS ON THE U NIT C IRCLE Objectives:  Graph an angle from a special triangle  Evaluate sine, cosine and tangent from a graph  Discover Unit Circle  Apply Properties of Unit Circle Vocabulary: standard position, sine, cosine, tangent, unit circle

Trigonometry & the Unit Circle

What is the Unit Circle? A perfect circle, centered at the origin (0,0) Used to find the trigonometric ratios of any angle that has a reference angle of 30, 45 or 60. Radius (hypotenuse) is ALWAYS 1.

Suppose an acute angle A is drawn in standard position as shown, point B (x, y) is a point on the terminal side. Right-Triangle-Based Definitions of Trigonometric Functions For any acute angle A in standard position, The Definition of Sine and Cosine Functions Since the concept of angle has been generalized, we generalize the above “Right-Triangle-Based” definition to formal trigonometric function definition.

Find Trig. Functions Using a Point on the Unit Circle b. 2 3

Find Trig. Functions Using a Point on the Unit Circle

If is a third-quadrant angle and sin is -5/13, find cos. R EMINDER :