Download Y12_1_Trig_Graphs

Trigonometry rules review
Use Soh Cah Toa
(o)
Opposite
Sin θ
x cm
(a)
Adjacent
(h)
Hypotenuse
Cos θ
(h)
Hypotenuse
1 cm
90°
20°
(o)
Opposite
Tan θ
(opposite
side)
(a)
Adjacent
Hypotenuse
(longest side)
h
o
θ
(adjacent side)
Sin θ
= the ratio
180°
0°
a
of the opposite side
the hypotenuse
270°
Calculators in
DEGREES
Generating the sin graph by rotating around a circle
90°
180°
x
0
30
60
90
120
150
180
210
Sinx
0°
270°
Trig Graphs: Introduction
The functions based on y = Sin(x), y = Cos(x), and y = Tan(x) produce trig
graphs.
The Sin & Cos graphs are periodic, described by the amplitude & period
Periodic: repeated cycle of values
sideways translation maps the graph back
onto itself
Period
(Wavelength)
Period: time taken for 1 cycle to pass
Length of 1 cycle = wavelength
Amplitude
Amplitude: half the ‘max y’ – ‘min y’
values (from the middle to top)
Basic Sin & Cos graphs have amplitude = 1
yy = Sin x
1
Theta
Ex34.01
1
90 180 270 360 x
-360 -270 -180 -90
-1
y = Cos x
y
90
-1
180
270
360 x
y
y
y
1
2
1
0.5
1.5
1
0.5
0.5
90
180
– 0.5
270
360 x
90
180
270
– 0.5
– 0.5
– 1
360 x
90
180
270
– 1
– 1
– 1.5
– 2
y = Sin(x)
Features
Amplitude
Period
Symmetry
Theta
Ex34.01
y = Cos(x)
Features
– 2.5
HW p153
y = Tan(x)
Features
360 x
Exploring the features of the graphs
y
1
1) Any angle with a negative ‘Cos’ value
must be between……
90
180
270
360 x
-1
2) If Cos(60°) = 0.5 what other angle is
possible for Cos(x°) = 0.5 (between 0 and 360°)
.5
.5
3) If Cos (x) = -0.4, what two angles (between 0 and 360°) are possible
y
2
For 0 < x < 90°
Sin(x)
Cos(x)
Tan(x)
For 90° < x < 180°
Sin(x)
Cos(x)
Tan(x)
1.5
1
0.5
– 0.5
– 1
90
180
270
360 x
For 180° < x < 270° Sin(x)
Cos(x)
Tan(x)
For 270° < x < 360°
Cos(x)
Tan(x)
– 1.5
– 2
– 2.5
Sin(x)