TRIGONOMETRY
Trigonometry comes from "treis" (three), "gonia" (angle) and "metron" (measurement) i.e. the
measurement of triangles.
Trigonometry was developed for use in astronomy and geography and has applications in
music, digital imaging, aircraft design and navigation, and modern architecture.
PART 1: TRIG IN RIGHT ANGLED TRIANGLES
A. Introduction
Naming triangles
Capital letters indicate angles and small letters indicate the side opposite the angle.
B
The side opposite the right-angle
(r) is called the hypotenuse
30
The symbol used to
indicate right-angle
Naming angles (using letters of the Greek alphabet)
a alpha beta theta
gamma phi delta
(The first row are the ones more commonly used.)
Trigonometry (Grade 10) Page
,Working with the right-angled triangle ABC
We will start by naming the sides relative to angle A. We are 'looking' from angle A.
.)O
Looking from angle A:
Hypotenuse
side BC is the
apposite side,
Opposite side AC is the
hypot couse and
side AB is the
Adjacent side.
B
Adjacent
Notice how the names of the sides change when looking from angle C.
C
Looking from angle C:
Hypotenuse u side
BC is the Ad @cent side
Adjacent side AC is the
hypateause and
B
side AB is the
opposite. side.
Opposite
Ratios SON CANTA
Since we are interested in forming ratios (fractions) in trigonometry, there are three ratios of
sides that we are particularly interested in.
opposite
S called sine. On the calculator it is written sin.
hypotenuse
adjacent
IS called cosine. On the calculator it is written cos.
hypotenuse
opposite
called tan. On the calculator it is written tan.
adjacent
Trigonometry (Grade 10) Page 2
, A little something to help you remember...
opposite Old
Some
hypotenuse Hens
And
COS ® Cackle
hypotenuse Howl
opposite Old
Till
adjacent Age
Let's recap:
h
Jo
Refer to the triangle PQR.
Determine: Are
we
a) sin Angie
trig finetion tee lan from
b) cos P
opp
c) tan R
A)sia P
HyP
✓
Pe Look at the diagram below and then complete the ratios for the given statements:
C
sin A cos B
AB
AB
Trigonometry (Grade 10) Page 3
, An Important Note
The size of a triangle makes no difference to the trig, ratios. This is illustrated in the figure
below:
F
2,45 cm
10 cm
In AABC: In AADE: In AAFG:
tan & = DE Fc
tan 0 = AG
=1,4 - 2.45
- 0,35
✓
0,35
V ✓
0,35
Calculator Work
What does sin 40° mean, and how do we 'calculate' this answer?
BE
.
opposite
We have already seen that sin is the ratio However, the value of this ratio varies
hypotenuse
based on the given angle, which is 40° here. (So sin40° gives us the corresponding ratio for an
angle of 40°.) We can use our calculator to give us the value of this ratio by pressing the
appropriate calculator keys.
Trigonometry (Grade 10) Page
Trigonometry comes from "treis" (three), "gonia" (angle) and "metron" (measurement) i.e. the
measurement of triangles.
Trigonometry was developed for use in astronomy and geography and has applications in
music, digital imaging, aircraft design and navigation, and modern architecture.
PART 1: TRIG IN RIGHT ANGLED TRIANGLES
A. Introduction
Naming triangles
Capital letters indicate angles and small letters indicate the side opposite the angle.
B
The side opposite the right-angle
(r) is called the hypotenuse
30
The symbol used to
indicate right-angle
Naming angles (using letters of the Greek alphabet)
a alpha beta theta
gamma phi delta
(The first row are the ones more commonly used.)
Trigonometry (Grade 10) Page
,Working with the right-angled triangle ABC
We will start by naming the sides relative to angle A. We are 'looking' from angle A.
.)O
Looking from angle A:
Hypotenuse
side BC is the
apposite side,
Opposite side AC is the
hypot couse and
side AB is the
Adjacent side.
B
Adjacent
Notice how the names of the sides change when looking from angle C.
C
Looking from angle C:
Hypotenuse u side
BC is the Ad @cent side
Adjacent side AC is the
hypateause and
B
side AB is the
opposite. side.
Opposite
Ratios SON CANTA
Since we are interested in forming ratios (fractions) in trigonometry, there are three ratios of
sides that we are particularly interested in.
opposite
S called sine. On the calculator it is written sin.
hypotenuse
adjacent
IS called cosine. On the calculator it is written cos.
hypotenuse
opposite
called tan. On the calculator it is written tan.
adjacent
Trigonometry (Grade 10) Page 2
, A little something to help you remember...
opposite Old
Some
hypotenuse Hens
And
COS ® Cackle
hypotenuse Howl
opposite Old
Till
adjacent Age
Let's recap:
h
Jo
Refer to the triangle PQR.
Determine: Are
we
a) sin Angie
trig finetion tee lan from
b) cos P
opp
c) tan R
A)sia P
HyP
✓
Pe Look at the diagram below and then complete the ratios for the given statements:
C
sin A cos B
AB
AB
Trigonometry (Grade 10) Page 3
, An Important Note
The size of a triangle makes no difference to the trig, ratios. This is illustrated in the figure
below:
F
2,45 cm
10 cm
In AABC: In AADE: In AAFG:
tan & = DE Fc
tan 0 = AG
=1,4 - 2.45
- 0,35
✓
0,35
V ✓
0,35
Calculator Work
What does sin 40° mean, and how do we 'calculate' this answer?
BE
.
opposite
We have already seen that sin is the ratio However, the value of this ratio varies
hypotenuse
based on the given angle, which is 40° here. (So sin40° gives us the corresponding ratio for an
angle of 40°.) We can use our calculator to give us the value of this ratio by pressing the
appropriate calculator keys.
Trigonometry (Grade 10) Page
