Angles of Any Magnitude

Angles of Any Magnitudey

x0

90

180

270

360

III

III IV

Angles of Any Magnitudey

x0

90

180

270

360

III

III IV

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

- normalQuadrant I

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

- normalQuadrant I

- 180Quadrant II

sin

cos

tan

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

- normalQuadrant I

- 180Quadrant II

sin

cos

tan

- 180Quadrant III

sin

cos

tan

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

- normalQuadrant I

- 180Quadrant II

sin

cos

tan

- 180Quadrant III

sin

cos

tan

- 360Quadrant IV

sin

cos

tan

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

- normalQuadrant I

- 180Quadrant II

sin

cos

tan

- 180Quadrant III

sin

cos

tan

- 360Quadrant IV

sin

cos

tan

e.g. sin 260 sin80i

0.9848

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

- normalQuadrant I

- 180Quadrant II

sin

cos

tan

- 180Quadrant III

sin

cos

tan

- 360Quadrant IV

sin

cos

tan

e.g. sin 260 sin80i

0.9848 tan 220 tan 40ii

0.8391

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

- normalQuadrant I

- 180Quadrant II

sin

cos

tan

- 180Quadrant III

sin

cos

tan

- 360Quadrant IV

sin

cos

tan

e.g. sin 260 sin80i

0.9848 tan 220 tan 40ii

0.8391

sec105 sec75iii

3.8637

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

- normalQuadrant I

- 180Quadrant II

sin

cos

tan

- 180Quadrant III

sin

cos

tan

- 360Quadrant IV

sin

cos

tan

e.g. sin 260 sin80i

0.9848 tan 220 tan 40ii

0.8391

sec105 sec75iii

3.8637 cos 430 cos70iv

0.3420

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

- normalQuadrant I

- 180Quadrant II

sin

cos

tan

- 180Quadrant III

sin

cos

tan

- 360Quadrant IV

sin

cos

tan

e.g. sin 260 sin80i

0.9848 tan 220 tan 40ii

0.8391

sec105 sec75iii

3.8637 cos 430 cos70iv

0.3420

tan 67 tan 293v

Angles of Any Magnitude

y

x0

90

180

270

360

III

III IV

- normalQuadrant I

- 180Quadrant II

sin

cos

tan

- 180Quadrant III

sin

cos

tan

- 360Quadrant IV

sin

cos

tan

e.g. sin 260 sin80i

0.9848 tan 220 tan 40ii

0.8391

sec105 sec75iii

3.8637 cos 430 cos70iv

0.3420

tan 67 tan 293v

tan 67

2.3559

(vi) Find the coordinates of Py

x

P30

5

(vi) Find the coordinates of Py

x

P30

5

cos305x

(vi) Find the coordinates of Py

x

P30

5

cos305x

5cos30x

5 32

x

(vi) Find the coordinates of Py

x

P30

5

cos305x

5cos30x

5 32

x

sin305y

(vi) Find the coordinates of Py

x

P30

5

cos305x

5cos30x

5 32

x

sin305y

5sin30y

52

y

5 3 5,2 2

P

(vi) Find the coordinates of Py

x

P30

5

cos305x

5cos30x

5 32

x

sin305y

5sin30y

52

y

5 3 5,2 2

P

Boundary Values

y

x0

90

180

270

(vi) Find the coordinates of Py

x

P30

5

cos305x

5cos30x

5 32

x

sin305y

5sin30y

52

y

5 3 5,2 2

P

Boundary Values

y

x0

90

180

270

01

9001

(vi) Find the coordinates of Py

x

P30

5

cos305x

5cos30x

5 32

x

sin305y

5sin30y

52

y

5 3 5,2 2

P

Boundary Values

y

x0

90

180

270

01

9001

sin 0 0

cos0 1

tan 0 0

0

(vi) Find the coordinates of Py

x

P30

5

cos305x

5cos30x

5 32

x

sin305y

5sin30y

52

y

5 3 5,2 2

P

Boundary Values

y

x0

90

180

270

01

9001

sin 0 0

cos0 1

tan 0 0

0

sin90 1

cos90 01tan900

90

undefined

(vi) Find the coordinates of Py

x

P30

5

cos305x

5cos30x

5 32

x

sin305y

5sin30y

52

y

5 3 5,2 2

P

Boundary Values

y

x0

90

180

270

01

9001

sin 0 0

cos0 1

tan 0 0

0

sin90 1

cos90 01tan900

90

undefined

sin180 0

cos180 1

tan180 0

180

(vi) Find the coordinates of Py

x

P30

5

cos305x

5cos30x

5 32

x

sin305y

5sin30y

52

y

5 3 5,2 2

P

Boundary Values

y

x0

90

180

270

01

9001

sin 0 0

cos0 1

tan 0 0

0

sin90 1

cos90 01tan900

90

undefined

sin180 0

cos180 1

tan180 0

180

sin 270 1

cos 270 01tan 270

0

270

undefined

Trigonometric Graphs

Trigonometric Graphs plot boundary values

Trigonometric Graphsy

x

-1

180 360 540 720180360

plot boundary values

Trigonometric Graphsy

x

1

-1

180 360 540 720180360

plot boundary values

Trigonometric Graphsy

x

1

-1

180 360 540 720180360

plot boundary values

Trigonometric Graphsy

x

1

-1

180 360 540 720180360

plot boundary values

Trigonometric Graphsy

x

sin xy 1

-1

180 360 540 720180360

plot boundary values

xrealall:domain11-:range y

period: 360

Trigonometric Graphsy

x

sin xy 1

-1

180 360 540 720180360

plot boundary values

xrealall:domain11-:range y

odd function sin sinx x

period: 360

Trigonometric Graphsy

x

sin xy 1

-1

180 360 540 720180360

plot boundary values

xrealall:domain11-:range y

odd function sin sinx x

y

x

1

-1

180 360 540 720180360

period: 360

Trigonometric Graphsy

x

sin xy 1

-1

180 360 540 720180360

plot boundary values

xrealall:domain11-:range y

odd function sin sinx x

y

x

1

-1

180 360 540 720180360

period: 360

Trigonometric Graphsy

x

sin xy 1

-1

180 360 540 720180360

plot boundary values

xrealall:domain11-:range y

odd function sin sinx x

y

x

1

-1

180 360 540 720180360

period: 360

Trigonometric Graphsy

x

sin xy 1

-1

180 360 540 720180360

plot boundary values

xrealall:domain11-:range y

odd function sin sinx x

y

x

cos y x1

-1

180 360 540 720180360

period: 360

Trigonometric Graphsy

x

sin xy 1

-1

180 360 540 720180360

plot boundary values

xrealall:domain11-:range y

odd function sin sinx x

y

x

cos y x1

-1

180 360 540 720180360

xrealall:domain11-:range y

period: 360

period: 360

Trigonometric Graphsy

x

sin xy 1

-1

180 360 540 720180360

plot boundary values

xrealall:domain11-:range y

odd function sin sinx x

y

x

cos y x1

-1

180 360 540 720180360

xrealall:domain11-:range y

even function cos cosx x

period: 360

period: 360

y

x180 360 540 720180360

y

x180 360 540 720180360

y

x

tan y x

180 360 540 720180360

y

x

tan y x

180 360 540 720180360

y

x

tan y x

180 360 540 720180360

domain: all real except 90 180 , where is an integerx x k k range: all real y

period: 180

y

x

tan y x

180 360 540 720180360

domain: all real except 90 180 , where is an integerx x k k range: all real y

odd function tan tanx x

period: 180

y

x

tan y x

180 360 540 720180360

domain: all real except 90 180 , where is an integerx x k k range: all real y

odd function tan tanx x

period: 180

x

cosec y x

1

-1180 360180360

y

y

x

tan y x

180 360 540 720180360

domain: all real except 90 180 , where is an integerx x k k range: all real y

odd function tan tanx x

period: 180

x

cosec y x

1

-1180 360180360

y

y

x

tan y x

180 360 540 720180360

domain: all real except 90 180 , where is an integerx x k k range: all real y

odd function tan tanx x

period: 180

x

cosec y x

1

-1180 360180360

y

y

x

tan y x

180 360 540 720180360

domain: all real except 90 180 , where is an integerx x k k range: all real y

odd function tan tanx x

period: 180

x

cosec y x

1

-1180 360180360

y

y

x

tan y x

180 360 540 720180360

domain: all real except 90 180 , where is an integerx x k k range: all real y

odd function tan tanx x

period: 180

x

cosec y x

1

-1180 360180360

y

y

x

tan y x

180 360 540 720180360

domain: all real except 90 180 , where is an integerx x k k range: all real y

odd function tan tanx x

period: 180

x

cosec y x

1

-1180 360180360

y

Exercise 4D; 3ace etc,4bdf etc, 5ace etc,

6bdf, 7ace, 8b, 9bd,10bd, 11ac,

13 ace etc, 14c, 16*