"We all marvel at the beauty of the Butterfly, but rarely take into account the changes it has undergone to get there."

- Axotlyorill

Chapter 2 Trigonometry

Section 2.1 Angles in Standard Position

Section 2.1

Page 83

Question 1

a) No; angle θ is not in standard position because its vertex is not at the origin.

b) Yes; angle θ is in standard position because its initial arm is on the positive x-axis and

the vertex is at the origin.

c) No; angle θ is not in standard position because its initial arm is not on the positive

x-axis.

d) Yes; angle θ is in standard position because its initial arm is on the positive x-axis and

the vertex is at the origin.

Section 2.1

Page 83

Question 2

a) Diagram F shows 150°.

b) Diagram C shows 180°.

c) Diagram A shows 45°.

d) Diagram D shows 320°.

e) Diagram B shows 215°.

f) Diagram E shows 270°.

Section 2.1

Page 83

Question 3

a) 48° is is quadrant I.

b) 300° is in quadrant IV.

c) 185° is in quadrant III.

d) 75° is in quadrant I.

e) 220° is in quadrant III.

f) 160° is in quadrant II.

MHR • Pre-Calculus 11 Solutions Chapter 2

Page 1 of 96

Section 2.1

Page 83

Question 4

a)

b)

c)

d)

Section 2.1

Page 83

Question 5

a) 180° − 170° = 10°. The reference angle for 170° is 10°.

b) 360° − 345° = 15°. The reference angle for 345° is 15°.

c) The reference angle for 72° is 72°.

d) 215° – 180° = 35°. The reference angle for 215° is 35°.

Section 2.1

Page 83

Question 6

a) 180° − 45° = 135°, 180° + 45° = 225°, 360° − 45° = 315°

The three other angles in standard position, 0° < θ < 360°, that have a reference angle of

45° are 135°, 225°, and 315°.

b) 180° − 60° = 120°, 180° + 60° = 240°, 360° − 60° = 300°

The three other angles in standard position, 0° < θ < 360°, that have a reference angle of

60° are 120°, 240°, and 300°.

c) 180° − 30° = 150°, 180° + 30° = 210°, 360° − 30° = 330°

The three other angles in standard position, 0° < θ < 360°, that have a reference angle of

30° are 150°, 210°, and 330°.

d) 180° − 75° = 105°, 180° + 75° = 255°, 360° − 75° = 285°

The three other...

Section 2.1 Angles in Standard Position

Section 2.1

Page 83

Question 1

a) No; angle θ is not in standard position because its vertex is not at the origin.

b) Yes; angle θ is in standard position because its initial arm is on the positive x-axis and

the vertex is at the origin.

c) No; angle θ is not in standard position because its initial arm is not on the positive

x-axis.

d) Yes; angle θ is in standard position because its initial arm is on the positive x-axis and

the vertex is at the origin.

Section 2.1

Page 83

Question 2

a) Diagram F shows 150°.

b) Diagram C shows 180°.

c) Diagram A shows 45°.

d) Diagram D shows 320°.

e) Diagram B shows 215°.

f) Diagram E shows 270°.

Section 2.1

Page 83

Question 3

a) 48° is is quadrant I.

b) 300° is in quadrant IV.

c) 185° is in quadrant III.

d) 75° is in quadrant I.

e) 220° is in quadrant III.

f) 160° is in quadrant II.

MHR • Pre-Calculus 11 Solutions Chapter 2

Page 1 of 96

Section 2.1

Page 83

Question 4

a)

b)

c)

d)

Section 2.1

Page 83

Question 5

a) 180° − 170° = 10°. The reference angle for 170° is 10°.

b) 360° − 345° = 15°. The reference angle for 345° is 15°.

c) The reference angle for 72° is 72°.

d) 215° – 180° = 35°. The reference angle for 215° is 35°.

Section 2.1

Page 83

Question 6

a) 180° − 45° = 135°, 180° + 45° = 225°, 360° − 45° = 315°

The three other angles in standard position, 0° < θ < 360°, that have a reference angle of

45° are 135°, 225°, and 315°.

b) 180° − 60° = 120°, 180° + 60° = 240°, 360° − 60° = 300°

The three other angles in standard position, 0° < θ < 360°, that have a reference angle of

60° are 120°, 240°, and 300°.

c) 180° − 30° = 150°, 180° + 30° = 210°, 360° − 30° = 330°

The three other angles in standard position, 0° < θ < 360°, that have a reference angle of

30° are 150°, 210°, and 330°.

d) 180° − 75° = 105°, 180° + 75° = 255°, 360° − 75° = 285°

The three other...

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