Post on 12-Aug-2015
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*