8/19/2019 Trigonometry Graph Eqn Appx Concise Notes
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H2 Mathematics
Call Mr Ong 9863 9633 for
Exam Qns and solutions
The General Solution of sin θ = sin α ,
where α is a known angle
degree)(in)1(180
radian)(in)1(
Z nn
Z nn
n
n
∈−+°=
∈−+=
α θ
α π θ
degree)(in)12(180 360 radian)(inm ,)12( ,2
ly,respectiveoddandeveniswhencaseheConsider t
Z mmor Z mm
Z mor Z mm
n
∈−+°=∈+°=
∈−+=∈+=
α θ α θ
α π θ α π θ
OR
The General Solution of cos θ = cos α ,
where α is a known angle
degree)(in360
radian)(in2
Z nn
Z nn
∈±°=
∈±=
α θ
α π θ
The General Solution of tan θ = tan α ,
where α is a known angle
degree)(in180radian)(in
Z nn
Z nn
∈+°=
∈+=
α θ
α π θ
Small Angles
θ θ
θ θ
θ θ
≈
−≈
≈
tan
2
11cos
sin
2
To draw the graph of bk x na y
)](sin[ where a, b, n and k are real,
(Multiply all the y-values by a )
(Determine the period of the functionn
2⇒ n cycles in the interval π 20
≤≤ x )
(Translate the graph k units in the posi ive x-direc
ion )
STEP 1: Sketch the graph of
STEP 2: Sketch the graph of
STEP 3: Sketch the graph of
STEP 4: Sketch the graph of
(Translate the graph b units in the posi ive y-direc
ion )
The same method is
used when sin is
replaced with cos or
tan.
Note:
Period isn
for tan
