[<< wikibooks] HSC Extension 1 and 2 Mathematics/Trigonometric functions
== Radian measure of an angle ==

== Arc length and area of a sector of a circle ==

l
=
r
θ

{\displaystyle l=r\theta \;}

A
=

1
2

r

2

θ

{\displaystyle A={\frac {1}{2}}r^{2}\theta }

== Area of a segment of a circle ==

=== Minor segment ===

A
=

1
2

r

2

(
θ
−
sin
⁡
θ
)

{\displaystyle A={\frac {1}{2}}r^{2}(\theta -\sin \theta )}

=== Major segment ===

A
=
π

r

2

−

1
2

r

2

(
θ
−
sin
⁡
θ
)

{\displaystyle A=\pi r^{2}-{\frac {1}{2}}r^{2}(\theta -\sin \theta )}

== Definitions of trigonometric functions ==
In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

== Symmetry properties of trigonometric functions ==

== Some exact values ==

== Graphs of trigonometric functions ==

== Graphs of y = a sin bx and y = a cos bx ==

== Graphs of y = a sin b(x + c) and y = a cos b(x + c) ==

== Graphical solution of equations ==

== Derivative of sin x and cos x ==

sin
′

⁡
x
=
cos
⁡
x

{\displaystyle \sin 'x=\cos x\;}

cos
′

⁡
x
=
−
sin
⁡
x

{\displaystyle \cos 'x=-\sin x\;}

== Derivative of tan x ==

tan
′

⁡
x
=

sec

2

⁡
x

{\displaystyle \tan 'x=\sec ^{2}x\;}

== Derivative of sin (ax + b) ==

sin
′

⁡
(
a
x
+
b
)
=
a
cos
⁡
(
a
x
+
b
)

{\displaystyle \sin '(ax+b)=a\cos(ax+b)\;}

== Derivative of cos (ax + b) ==

cos
′

⁡
(
a
x
+
b
)
=
−
a
sin
⁡
(
a
x
+
b
)

{\displaystyle \cos '(ax+b)=-a\sin(ax+b)\;}

== Functions defined by integrals (indefinite integrals) ==

== Primitives of trigonometric functions ==

=== Approximate integration ===