Lesson Notes 8-5
The Cosine Rule
We found the sine rule useful when
there was not a 90 angle, and
we knew one angle and its opposite side
Now, we will find the cosine rule useful when:
there is not a 90 angle, and
either
a) we know all three sides and

Lesson Notes 9-3
Trigonometric Identities
Identities are special kinds of equations that are true for ALL values of x. You are
already familiar with two identities:
sin2 + cos2 = 1
tan =
There are also some double-angle identities:
cos(2) = 1 2sin2
= 2cos

Lesson Notes 9-2
Solving Equations Using the Unit Circle
To solve for angles given their sine, cosine, or tangent values:
Step 1: Determine which quadrants the solution(s) will be in by looking at the
sign (+ or -) of the given ratio.
Step 2: Solve for th

Lesson Notes 8-4
The Sine Rule
Determine h in the following triangle
The Sine Rule
sin A sin B sinC
=
=
a
b
c
a
b
c
=
=
sin A sin B sinC
Example 1: Determine b.
C
A
B
D
b
13m
71
A
29
17m
B
Example 2: Determine angle A.
4)
C
8m
11 m
45
A
B
Example 3: A shi

Lesson Notes 8-7
Radians, Arcs, and Sectors
Angles can be measured in radians instead of degrees. One radian is defined as the size
of the central angle subtended by an arc which is the same length as the radius of the
circle.
Two radians is the size of t

Lesson Notes 8-1
Right-Angled Triangle Trigonometry
Angles can be described in various ways. The following triangle could be called ABC
and the angle at A could be called A, BAC, CAB, BAC, or CAB. Angles can also be
labeled with Greek letters like (theta)

Lesson Notes 8-2
Applications of Right-Angled Trigonometry
In this lesson, you will see how to apply these trigonometric ratios to solve problems in
real-life situations. Lets begin with some terminology
The angle of elevation is
The angle of depression i

Lesson Notes 8-3
Using the Coordinate Axes in Trigonometry
The angle in a Cartesian coordinate system has its vertex at the origin, as shown in the
diagram. A positive angle is measured anticlockwise from the x-axis.
The following diagram shows a circle w

Lesson Notes 9-1
Using the Unit Circle
On a Cartesian plane, you can generate an angle by rotating a ray about the origin. The
starting position of the ray, along the positive x-axis, is the initial arm of the angle. The
final position, after a rotation a

Pascals Triangle & the Binomial Expansion
Lesson Notes 7-9
Now we will look at a famous mathematical pattern know as Pascals triangles.
1
1
1
1
1
1
2
3
4
1
3
6
1
4
1
These numbers can also be found using combinations, or the nCr function on the GDC.
4C0
=