quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position...

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Transcript of quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position...

Page 1: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero
Page 2: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

• quadrantal angle

• reference angle

• unit circle

• circular function

• periodic function

• period

Page 3: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero
Page 4: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Evaluate Trigonometric Functions Given a Point

Let (–4, 3) be a point on the terminal side of an angle θ

in standard position. Find the exact values

of the six trigonometric functions of θ.

Page 5: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Let (–3, 6) be a point on the terminal side of an angle Ө

in standard position. Find the exact values

of the six trigonometric functions of Ө.

Page 6: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero
Page 7: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Evaluate Trigonometric Functions of Quadrantal Angles

A. Find the exact value of cos π. If not defined, write undefined.

Page 8: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Evaluate Trigonometric Functions of Quadrantal Angles

B. Find the exact value of tan 450°. If not defined, write undefined.

Page 9: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Evaluate Trigonometric Functions of Quadrantal Angles

C. Find the exact value of . If not defined, write undefined.

Page 10: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Find the exact value of sec If not defined, write undefined.

Page 11: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero
Page 12: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero
Page 13: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Find Reference Angles

A. Sketch –150°. Then find its reference angle.

Answer: 30°

Page 14: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Find Reference Angles

Answer:

B. Sketch . Then find its reference angle.

Page 15: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Find the reference angle for a 520o angle.

Page 16: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero
Page 17: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Use Reference Angles to Find Trigonometric Values

A. Find the exact value of .

Page 18: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Use Reference Angles to Find Trigonometric Values

B. Find the exact value of tan 150º.

Page 19: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Use Reference Angles to Find Trigonometric Values

C. Find the exact value of .

Page 20: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

Find the exact value of cos .

Page 21: quadrantal angle · Trigonometric Functions of Any Angle Let O be any angle in standard position and point P(x, y) be a point on the terminal side of O. Let r represent the nonzero

End of lesson 1, beginning of lesson 2