Introduction to Trigonometry

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Presentation transcript:

Introduction to Trigonometry Trig Ratios in the Coordinate Plane

Reference Angle: the positive acute angle formed by the terminal side and the closest x-axis. QUADRANT I QUADRANT II QUADRANT III QUADRANT IV

Draw the Reference Triangle for each Quadrant QUADRANT I QUADRANT II QUADRANT III QUADRANT IV

S A T C Positive Trig Functions and their Quadrants ALWAYS DOUBLE-CHECK THE SIGNS OF YOUR ANSWERS!!! Positive Trig Functions and their Quadrants S A T C All Students Take Calculus! All Super Tacos Crunch!

Positive Trig Functions and their Quadrants Sine Cosecant All Tangent Cotangent Cosine Secant All Students Take Calculus! All Super Tacos Crunch!

FINDING TRIG VALUES GIVEN A POINT Plot the point. Draw the reference triangle. Label the sides. EX: The point (3, 4) is on the terminal side of an angle Θ. Find the 6 trig values of Θ.

FINDING TRIG VALUES GIVEN A POINT Plot the point. Draw the reference triangle. Label the sides. EX: The point (-5, 12) is on the terminal side of an angle Θ. Find the 6 trig values of Θ.

FINDING TRIG VALUES GIVEN A POINT Plot the point. Draw the reference triangle. Label the sides. EX: The point (-8, -15) is on the terminal side of an angle Θ. Find the 6 trig values of Θ.

FINDING TRIG VALUES GIVEN A POINT Plot the point. Draw the reference triangle. Label the sides. EX: The point (7, -24) is on the terminal side of an angle Θ. Find the 6 trig values of Θ.

FINDING TRIG VALUES GIVEN A TRIG RATIO AND QUADRANT Draw the reference triangle. Use the trig ratio to label its sides. EX: Suppose and the terminal side of the angle lies in Quadrant I. Find the value of the other 5 trig functions.

FINDING TRIG VALUES GIVEN A TRIG RATIO AND QUADRANT Draw the reference triangle. Use the trig ratio to label its sides. EX: Suppose and the terminal side of the angle lies in Quadrant III. Find the value of the other 5 trig functions.

FINDING TRIG VALUES GIVEN A TRIG RATIO AND QUADRANT Draw the reference triangle. Use the trig ratio to label its sides. EX: Suppose and the terminal side of the angle lies in Quadrant II. Find the value of the other 5 trig functions.

FINDING TRIG VALUES GIVEN A TRIG RATIO AND QUADRANT Draw the reference triangle. Use the trig ratio to label its sides. EX: Suppose and the terminal side of the angle lies in Quadrant IV. Find the value of the other 5 trig functions.