11 x1 t04 01 trigonometric ratios (2010)
TRANSCRIPT
Trigonometric Ratios
Trigonometric Ratios hypotenuse
adjacent
opposite
Trigonometric Ratios hypotenuse
sin opphyp
adjacent
opposite
cos adjhyp
tan oppadj
Trigonometric Ratios hypotenuse
sin opphyp
adjacent
opposite
cos adjhyp
tan oppadj
cosec hypopp
sec hypadj
cot adjopp
Trigonometric Ratios hypotenuse
sin opphyp
adjacent
opposite
cos adjhyp
tan oppadj
cosec hypopp
sec hypadj
cot adjopp
e.g. sin cos 25i x
Trigonometric Ratios hypotenuse
sin opphyp
adjacent
opposite
cos adjhyp
tan oppadj
cosec hypopp
sec hypadj
cot adjopp
e.g. sin cos 25i x
90 25x 65x
Trigonometric Ratios hypotenuse
sin opphyp
adjacent
opposite
cos adjhyp
tan oppadj
cosec hypopp
sec hypadj
cot adjopp
e.g. sin cos25i x
90 25x 65x
cot 20 tan 30ii x x
Trigonometric Ratios hypotenuse
sin opphyp
adjacent
opposite
cos adjhyp
tan oppadj
cosec hypopp
sec hypadj
cot adjopp
e.g. sin cos25i x
90 25x 65x
cot 20 tan 30ii x x 20 30 90x x
2 8040
xx
iii
a
1361
iii
a
1361
tan 6113a
iii
a
1361
tan 6113a
13tan 61a
23.5 units (to 1 dp)a
iii
a
1361
tan 6113a
13tan 61a
23.5 units (to 1 dp)a
iv
x
5
32
iii
a
1361
tan 6113a
13tan 61a
23.5 units (to 1 dp)a
iv
x
5
32
5 sin32x
iii
a
1361
tan 6113a
13tan 61a
23.5 units (to 1 dp)a
iv
x
5
32
5 sin32x
5sin32
x
9.4 units (to 1 dp)x
iii
a
1361
tan 6113a
13tan 61a
23.5 units (to 1 dp)a
iv
x
5
32
5 sin32x
5sin32
x
9.4 units (to 1 dp)x
v
10
14
iii
a
1361
tan 6113a
13tan 61a
23.5 units (to 1 dp)a
iv
x
5
32
5 sin32x
5sin32
x
9.4 units (to 1 dp)x
v
10
14
10cos14
iii
a
1361
tan 6113a
13tan 61a
23.5 units (to 1 dp)a
iv
x
5
32
5 sin32x
5sin32
x
9.4 units (to 1 dp)x
v
10
14
10cos14
1 10cos14
44 25
Exact Ratios
60
60
60
Exact Ratios
22
260
60
60
Exact Ratios
2
160
303
Exact Ratios
2
160
303
1sin302
3cos302
1tan303
Exact Ratios
2
160
303
1sin302
3cos302
1tan303
3sin 602
1cos602
tan 60 3
Exact Ratios
2
160
303
1sin302
3cos302
1tan303
3sin 602
1cos602
tan 60 3
45
451
12
Exact Ratios
2
160
303
1sin302
3cos302
1tan303
3sin 602
1cos602
tan 60 3
45
451
12
1sin 452
1cos 452
tan 45 1
Alternative way of remembering the exact ratios
sin
cos
tan
0 30 45 60 90
Alternative way of remembering the exact ratios
sin
cos
tan
0 30 45 60 90
02
12
22
32
42
Alternative way of remembering the exact ratios
sin
cos
tan
0 30 45 60 90
02
12
22
32
42
42
32
22
12
02
Alternative way of remembering the exact ratios
sin
cos
tan
0 30 45 60 90
02
12
22
32
42
42
32
22
12
02
sincos
Alternative way of remembering the exact ratios
sin
cos
tan
0 30 45 60 90
02
12
22
32
42
42
32
22
12
02
sincos
04
13
22
31
40
Measuring Angles
Measuring AnglesAngle of Elevation
A
B
Measuring AnglesAngle of Elevation
A
B
angle of elevation of B from A
Measuring AnglesAngle of Elevation
A
B
angle of elevation of B from A
Angle of Depression
X
Y
Measuring AnglesAngle of Elevation
A
B
angle of elevation of B from A
Angle of Depression
X
Y
angle of depresion of X from Y
Measuring AnglesAngle of Elevation
A
B
angle of elevation of B from A
Angle of Depression
X
Y
angle of depresion of X from Y
Note: angle of elevation = angle of depression
Measuring AnglesAngle of Elevation
A
B
angle of elevation of B from A
Angle of Depression
X
Y
angle of depresion of X from Y
Note: angle of elevation = angle of depression
Compass Bearings N
S
EW
Measuring AnglesAngle of Elevation
A
B
angle of elevation of B from A
Angle of Depression
X
Y
angle of depresion of X from Y
Note: angle of elevation = angle of depression
Compass Bearings N
S
EW
NE
SESW
NW
Measuring AnglesAngle of Elevation
A
B
angle of elevation of B from A
Angle of Depression
X
Y
angle of depresion of X from Y
Note: angle of elevation = angle of depression
Compass Bearings N
S
EW
NE
SESW
NW NNE
ENE
ESE
SSESSW
WSW
WNW
NNW
True BearingsAlways start NORTH and measure clockwise
True BearingsAlways start NORTH and measure clockwise
X
Y
True BearingsAlways start NORTH and measure clockwise
X
Y
Bearing of Y from X
True BearingsAlways start NORTH and measure clockwise
N
X
Y
30
Bearing of Y from X
True BearingsAlways start NORTH and measure clockwise
N
X
Y
30
Bearing of Y from X120 T
or S60 E
True BearingsAlways start NORTH and measure clockwise
N
X
Y
30
Bearing of Y from X120 T
or S60 E
Bearing of X from Y
True BearingsAlways start NORTH and measure clockwise
N
X
Y
30
Bearing of Y from X120 T
or S60 E
Bearing of X from Y
N
60
True BearingsAlways start NORTH and measure clockwise
N
X
Y
30
Bearing of Y from X120 T
or S60 E
Bearing of X from Y300 T
or N60 W
N
60
Exercise 4A; 1 to 3 (pick some), 4acf, 5, 7bd, 8ac, 9bd, 11, 12,14c, 17, 18, 19b, 21, 23, 24, 25
Exercise 4B; 1b, 2b, 3, 4b, 6, 7, 10