Download - 11 x1 t04 02 angles of any magnitude (2013)
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Angles of Any Magnitude
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Angles of Any Magnitudey
x0
90
180
270
360
III
III IV
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Angles of Any Magnitudey
x0
90
180
270
360
III
III IV
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Angles of Any Magnitude
y
x0
90
180
270
360
III
III IV
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Angles of Any Magnitude
y
x0
90
180
270
360
III
III IV
- normalQuadrant I
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Angles of Any Magnitude
y
x0
90
180
270
360
III
III IV
- normalQuadrant I
- 180Quadrant II
sin
cos
tan
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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
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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
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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
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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
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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
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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
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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
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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
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(vi) Find the coordinates of Py
x
P30
5
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(vi) Find the coordinates of Py
x
P30
5
cos305x
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(vi) Find the coordinates of Py
x
P30
5
cos305x
5cos30x
5 32
x
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(vi) Find the coordinates of Py
x
P30
5
cos305x
5cos30x
5 32
x
sin305y
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(vi) Find the coordinates of Py
x
P30
5
cos305x
5cos30x
5 32
x
sin305y
5sin30y
52
y
5 3 5,2 2
P
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(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
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(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
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(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
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(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
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(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
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(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
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Trigonometric Graphs
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Trigonometric Graphs plot boundary values
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Trigonometric Graphsy
x
-1
180 360 540 720180360
plot boundary values
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Trigonometric Graphsy
x
1
-1
180 360 540 720180360
plot boundary values
![Page 30: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/30.jpg)
Trigonometric Graphsy
x
1
-1
180 360 540 720180360
plot boundary values
![Page 31: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/31.jpg)
Trigonometric Graphsy
x
1
-1
180 360 540 720180360
plot boundary values
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Trigonometric Graphsy
x
sin xy 1
-1
180 360 540 720180360
plot boundary values
xrealall:domain11-:range y
period: 360
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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
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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
![Page 35: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/35.jpg)
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
![Page 36: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/36.jpg)
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
![Page 37: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/37.jpg)
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
![Page 38: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/38.jpg)
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
![Page 39: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/39.jpg)
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
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y
x180 360 540 720180360
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y
x180 360 540 720180360
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y
x
tan y x
180 360 540 720180360
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y
x
tan y x
180 360 540 720180360
![Page 44: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/44.jpg)
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
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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
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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
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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
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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
![Page 49: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/49.jpg)
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
![Page 50: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/50.jpg)
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
![Page 51: 11 x1 t04 02 angles of any magnitude (2013)](https://reader033.vdocuments.us/reader033/viewer/2022042701/55caa544bb61eb8b5d8b47f1/html5/thumbnails/51.jpg)
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*