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Formula Sheets
/ Maths
Chapter 10
Trigonometric Equations
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Download this chapter (PDF)
All Maths formulas (PDF)
General solutions
a cos θ + b sin θ = c
Principal values and inequalities
General solutions
sin
θ
=
0
⇒
θ
=
nπ
;
cos
θ
=
0
⇒
θ
=
(
2
n
+
1
)
2
π
;
tan
θ
=
0
⇒
θ
=
nπ
sin
θ
=
sin
α
⇒
θ
=
nπ
+
(
−
1
)
n
α
cos
θ
=
cos
α
⇒
θ
=
2
nπ
±
α
;
tan
θ
=
tan
α
⇒
θ
=
nπ
+
α
sin
2
θ
=
sin
2
α
,
cos
2
θ
=
cos
2
α
,
tan
2
θ
=
tan
2
α
⇒
θ
=
nπ
±
α
In all of these,
n
∈
Z
.
a cos θ + b sin θ = c
divide by
a
2
+
b
2
:
cos
(
θ
−
ϕ
)
=
a
2
+
b
2
c
,
tan
ϕ
=
a
b
Solvable only when
∣
c
∣
≤
a
2
+
b
2
.
Principal values and inequalities
Principal solution
solutions in
[
0
,
2
π
)
Inequalities
solve on one period using the graph, then add the period
Example:
sin
x
>
2
1
⇒
x
∈
(
2
nπ
+
6
π
,
2
nπ
+
6
5
π
)
.
Trigonometric Ratios and Identities
Inverse Trigonometric Functions