Introduction to Trigonometry

1
Lets Investigate
The Tangent Ratio
The Tangent Angle
The Sine Ratio
The Sine Angle
The Cosine Ratio
The Cosine Angle
Mixed Problems
Extension
2
Starter Questions
www.mathsrevision.com
3
Lets Investigate!
Trigonometry
4
Trigonometry means triangle and measurement.
We will be using right-angled triangles.

Opposite
hypotenuse
x
Adjacent
5
Mathemagic!
Opposite
hypotenuse
30
Adjacent
Opposite

0.6
Adjacent
6
Try another!
Opposite
hypotenuse
45
Adjacent
Opposite

1
Adjacent
7
For an angle of 30,
We write tan 30 0.6
8
Tan 25 0.466
Tan 26 0.488
Tan 27 0.510
Tan 28 0.532
Tan 29 0.554
Tan 30 0.577
Tan 31 0.601
Tan 32 0.625
Tan 33 0.649
Tan 34 0.675
Accurate to 3 decimal places!
9
On your calculator press
Tan
Followed by 30, and press

Notice that your calculator is incredibly
accurate!!
Accurate to 9 decimal places!
10
(No Transcript)
11
How high is the tower?
60
12 m
12
Opposite
hypotenuse
60
12 m
Adjacent
13
Opp
Tan x
Adj
Opp
Tan 60
12
Opp
12 x Tan 60
Opp
12 x Tan 60
20.8m (1 d.p.)
14
?
So the towers 20.8 m high!
15
Starter Questions
3cm
www.mathsrevision.com
16
Opp
Tan x
Adj
Opposite
x
Adjacent
17
Example
Opp
Hyp
Opp
c
Tan x
Adj
65
c
Tan 65
8m
8
Adj
c
8 x Tan 65
c
8 x Tan 65
17.2m (1 d.p.)
18
Now try Exercise 1. (HSDU Support Materials)
19
Starter Questions
www.mathsrevision.com
20
Using Tan to calculate angles
21
Example
SOH CAH TOA
Opp
Hyp
18m
Opp
?
Tan x
Adj
x
12m
18
Tan x
Adj
12
1.5
Tan x
22
How do we find x?
Tan ?¹is written above
Followed by
2nd
To get this press
Tan
23
2nd
Press
Enter

1.5
Tan ?¹1.5
x
56.3 (1 d.p.)
24
Now try Exercise 2. (HSDU Support Materials)
25
Starter Questions
www.mathsrevision.com
26
The Sine Ratio
Opp
Sin x
Hyp
Opposite
hypotenuse
x
27
Example
Hyp
11cm
O
Opp
Opp
Sin x
34
Hyp
O
Sin 34
11
O
11 x Sin 34
O
11 x Sin 34
6.2cm (1 d.p.)
28
Now try Exercise 3. (HSDU Support Materials)
29
Starter Questions
www.mathsrevision.com
57o
30
Using Sin to calculate angles
31
Example
Hyp
9m
6m
SOH CAH TOA
Opp
x
Opp
?
Sin x
Hyp
6
Sin x
9
0.667 (3 d.p.)
Sin x
32
How do we find x?
Sin ?¹is written above
Sin
Followed by
2nd
To get this press
33
Press
2nd
Enter
0.667

x
Sin ?¹0.667
41.8 (1 d.p.)
34
Now try Exercise 4. (HSDU Support Materials)
35
Starter Questions
www.mathsrevision.com
36
The Cosine Ratio
Adj
Cos x
Hyp
hypotenuse
x
Adjacent
37
Example
b
Adj
40
Adj
Cos x
Opp
Hyp
Hyp
35mm
b
Cos 40
35
b
35 x Cos 40
b
35 x Cos 40
26.8mm (1 d.p.)
38
Now try Exercise 5. (HSDU Support Materials)
39
Starter Questions
Q1. Calculate
Q2. Round to 1 decimal place 2.354.
Q3. How many minutes in 3hours
www.mathsrevision.com
Q4. The answer to the question is 180. What is
the question.
40
Using Cos to calculate angles
41
Example
SOH CAH TOA
Adj
34cm
x
Adj
Cos x
Opp
Hyp
Hyp
45cm
34
Cos x
45
0.756 (3 d.p.)
Cos x
x
Cos ?¹0.756
40.9 (1 d.p.)
42
Now try Exercise 6. (HSDU Support Materials)
43
Starter Questions
www.mathsrevision.com
44
The Three Ratios
Sine
Tangent
Cosine
Sine
Sine
Tangent
www.mathsrevision.com
Cosine
Cosine
Sine
45
The Three Ratios
46
(No Transcript)
47
Mixed Examples
Cos 20
Tan 27
Sin 36
Sin 60
Sin 30
Tan 40
www.mathsrevision.com
Cos 12
Cos 79
Sin 35
48
Example 1
SOH CAH TOA
Hyp
15m
O
Opp
Opp
Sin x
40
Hyp
O
Sin 40
15
O
15 x Sin 40
O
15 x Sin 40
9.6m (1 d.p.)
49
Example 2
SOH CAH TOA
b
Adj
35
Adj
Opp
Cos x
Hyp
Hyp
23cm
b
Cos 35
23
b
23 x Cos 35
b
23 x Cos 35
18.8cm (1 d.p.)
50
Example 3
SOH CAH TOA
Opp
Hyp
c
Opp
Tan x
Adj
60
c
15m
Tan 60
15
Adj
c
15 x Tan 60
c
15 x Tan 60
26.0m (1 d.p.)
51
Now try Exercise 7. (HSDU Support Materials)
52
Starter Questions
Level E
www.mathsrevision.com
53
Extension
www.mathsrevision.com
54
Example 1
Hyp
b
23cm
Opp
SOH CAH TOA
30
Opp
?
Sin x
Hyp
23
Sin 30
b
55
23
Sin 30
b
23
b
Sin 30
(This means b 23 Sin 30º)
b
46 cm
56
Example 2
SOH CAH TOA
7m
Adj
50
Adj
Opp
Cos x
Hyp
Hyp
p
7
Cos 50
p
7
p
Cos 50
p
10.9m (1 d.p.)
57
Example 3
SOH CAH TOA
Opp
Hyp
Opp
9m
Tan x
Adj
55
9
Tan 55
d
Adj
d
9
d
Tan 55
d
6.3m (1 d.p.)