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 Vocabulary: standard position, sine, cosine, tangent, 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.

Filling out unit circle Activity! Cut out and label your and triangles with their corresponding lengths ON BOTH SIDES!!!

The Triangle

The Triangle 30 60

Think Back: Reference Angles Reference angles allow us to easily find the sine/cosine of angles outside of Quadrant I If we know the sine/cosine/tangent for our and triangle, we can find trig ratios for all the other “common” angles in our unit circle

What is reference angle of each? **If given in radians, stay in radians!

Filling out unit circle Activity! Cut out and label your and triangles with their corresponding lengths ON BOTH SIDES!!! Label the signs of your unit circle quadrants. Use these triangles to find the value of sine, cosine and tangent at each angle’s point of intersection with the unit circle.

Signs of Trig. Functions on Unit Circle Where are the trig. functions positive? All Sine Tangent Cosine

Also true for Reciprocal Identities!!!

Evaluate the Trig. Functions NO CALCULATOR 1 0 Undefined

Homework pg. 279 #2 (just state the reference angle) pg. 280 #14-16 **NO CALCULATORS!

Warm Up Please complete the following on a half sheet of paper. 1.) State whether the expression is positive or negative: a) sin(192˚)b) cos(281˚) 2.) Find the sine, cosine, and tangent of the angle that’s formed by the following point: (3, -4) **Remember: All Students Take Calculus!