PART 1 TRIGONOMETRIC FUNCTION SOH CAH TOA

Understand the fundamental of trigonometric
functions

Opposite Right Angle Triangle

Hypotenuse



Adjacent

Hypotenuse
• The side which is opposite the right angle (90 ˚) and

it is the longest side.

Opposite Side
• Opposite to the angle

Adjacent side
• Adjacent (next to) to the angle

Understand the fundamental of trigonometric
functions

Define of Sine, cosine, tangent

Sine Cosine

Opposite Hypotenuse Hypotenuse


sin  opposite Adjacent
hypotenuse
cos  adjacent
SOH hypotenuse
CAH
Tangent
sin
Opposite tan = cos



Adjacent

tan  opposite
adjacent

TOA

Understand the fundamental of trigonometric
functions

Define of Cosecant, Secant, Cotangent

Cosecant Secant
Cosecant
Sec
cos
1 1
= cos
= sin
ℎ ℎ
=
=

Cotangent cos
cot = sin
Cot

1
= tan


=

Understand the fundamental of trigonometric
functions

Pythagorean Theorem Formula

Pythagorean Theorem Formula

2 = 2 + 2

Hypotenuse, H

Opposite, O



THE RIGHT ANGLE
TRIANGLE

Adjacent, A

TISGTOENPOBYMSETTERPICTOFUSNOCLTVIOE N

STEP 1 Label the opposite side (O), adjacent
side (A) and hypotenuse (H) of the

right angled triangle.

STEP 2 Find missing sides in right angled
triangles by using Pythagorean Theorem.

2 = 2 + 2

i. Choose the trigonometric ratio

depends on the question.

STEP 3 1
sin = cosec = sin

1
cos = sec = cos

1
tan = cot = tan

ii. Substitute the side lengths into the
correct formula triangle.

iii. Complete the calculation to find your
answer.

Example 1
P

9cm 15cm


R

Q

The right-angled triangle PQR in the figure above shows

that PQ=9cm and PR=15cm . Calculate:

a) sin θ d) cot θ
b) cos θ e) sec θ
c) tan θ f) cosec θ

Example 2

Given that tan = 5 , and is acute angle .
12

Without using the calculator, find the values of:

a) cos θ d) sec θ

b) sin θ e) cosec θ

c) cot θ

Example 1

01 Label O, A, H of the right 03a) θ= = 9 3
angled triangle. sin 15 = 5
P
= 12 4
b) cos θ= 15 = 5

O H c) tan θ= = 9 = 3
12 4
9cm 15cm
Q
d) cot θ= 1
tan
A R
1

=3

4

02 Find missing sides in =4
right angled triangles by
using Pythagorean 3
Theorem
e) sec θ= 1
2 = 2 + 2 cos
1
152 = 2 +92 =4
225 = 2 +81
2 = 225 − 81 5

2 = 144 = 4
3
= 144 1
= 12 f) cosec θ= sin

1

=3

5

= 5
3

Example 2

Sketch the right angle 03

01 triangle and then label O, a) cos θ= = 12
A, H of the right angled 13
triangle.

tan = 5 =
12
sin θ= = 5
P b) 13

H 1
O tan

5cm c) cot θ=

1

Q R =5
12cm A
12

= 12
5
Find missing sides in
d) sec θ= 1
02 right angled triangles by cos
using Pythagorean 1
Theorem = 12
2 = 2 + 2
13
2 = 122 +52
2 = 144 + 25 = 13
12
2 = 169 1
= 169 e) cosec θ= sin
= 13
1

=5

13

= 13
5

Example 3
D

E
20cm


A 7cm B C

Given sin = 3 and E is the midpoint BD. Calculate
5

cos and .

Example 4

From the right-angled triangle ABC in the figure

below, given that cot = 0.577 and = 4 .

Determine: C

A
B 4 units

a)the value of the angle θ

b)the perimeter of the triangle.

Example 3

01 Label O, A, H of the right 02 D
angled triangle.
D H 24cm

O

E
A
O H 7cm B
20cm
A 7cm B A

A C 2 = 2 + 2

02 Find missing sides in right 2 = 72 +242
angled triangles by using 2 = 49 + 576
Pythagorean Theorem
2 = 625
sin = 3
5 = 625
= 25

=

3 = 03cos y= = 7
5 20 25

20 × 3 sec θ= 1
= 5
= 12 cos

= = = 12 1
= 12 + 12 = 24
=7

25

25
=7

Example 4

01 Label O, A, H of the right 03 Find the perimeter
angled triangle. of the triangle
C
cos θ= = 12
H
O 13

cos 600 = 4
B 4 units A

A H= cos 4

60.020

H= 8

02 Find the value of the 2 = 2 + 2
angle θ
82 = 42 + 2
cot = 0.577 2 = 64 − 16

1 = 0.577 2 = 48
tan = 48
1 = 6.9
tan =
0.577 Perimeter=AB+BC+AC
= −1 1 =4+8+6.9
0.577 =18.9cm

= 600

QUIZ

P

24cm



Maximize this space for 10cm N

Madditional resources you

want to share with your

Thesrtuidgehntts.-angled triangle MNP in the figure above

shows that MN=10cm and PN=24cm . Calculate:

a) sin θ d) cot θ
b) cos θ e) sec θ
c) tan θ f) cosec θ

Given that cos = 8 , and is acute angle .
12

Without using the calculator, find the values of:

a) cos θ d) sec θ

b) sin θ e) cosec θ

c) cot θ

QUIZ

18cm


D

Maximize this space for 30cm
additional resources you C
want to share with your

students.

In the diagram, tan = 3 . Find the value of sin .
4

From the right-angled triangle ABC in the figure

below, given that cosec = 0.5 and = 5 .

Determine: A B

5 units

C
a)the value of the angle θ
b)the perimeter of the triangle.