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Trigonometry

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Trigonometry Learning Objective: To be able to describe the sides of right-angled triangle for use in trigonometry. Trigonometry is concerned with the connection ... – PowerPoint PPT presentation

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Title: Trigonometry


1
12 July 2015
Trigonometry
Learning Objective To be able to describe the
sides of right-angled triangle for use in
trigonometry.
Trigonometry is concerned with the connection
between the sides and angles in any right angled
triangle.
2
The sides of a right -angled triangle are given
special names The hypotenuse, the opposite and
the adjacent. The hypotenuse is the longest side
and is always opposite the right angle. The
opposite and adjacent sides refer to another
angle, other than the 90o.
3
There are three formulae involved in
trigonometry sin A cos
A tan A
S O H C A H T O A
4
Using trigonometry on the calculator
12 July 2015
Learning Objective To be able to use a
scientific calculator to find decimal values and
angles in trigonometry.
All individual angles have different sine, cosine
and tangent ratios (or decimal values).
Scientific calculators store information about
every angle. We need to be able to access this
information in the correct manner.
5
Finding the ratios
The simplest form of question is finding the
decimal value of the ratio of a given angle.
  • Find
  • sin 32

sin
32
  1. cos 23
  2. tan 78
  3. tan 27
  4. sin 68

6
Using ratios to find angles
We have just found that a scientific calculator
holds the ratio information for sine (sin),
cosine (cos) and tangent (tan) for all
angles. It can also be used in reverse, finding
an angle from a ratio. To do this we use the
sin-1, cos-1 and tan-1 function keys.
7
  • Example
  • sin x 0.1115 find angle x.

sin-1
0.1115

x sin-1 (0.1115) x 6.4o
2. cos x 0.8988 find angle x
cos-1
0.8988

x cos-1 (0.8988) x 26o
8
12 July 2015
Trigonometry
Learning Objective To be able to use
trigonometry to find the unknown angle in a
triangle.
9
Finding an angle from a triangle
To find a missing angle from a right-angled
triangle we need to know two of the sides of the
triangle. We can then choose the appropriate
ratio, sin, cos or tan and use the calculator to
identify the angle from the decimal value of the
ratio.
Find angle C
  • Identify/label the names of the sides.
  • b) Choose the ratio that contains BOTH of the
    letters.

10
H
A
Cos C 0.4286
C cos-1 (0.4286) C 64.6o
11
A
O
Tan x 2.6667
x tan-1 (2.6667) x 69.4o
12
sin x 0.8333
x sin-1 (0.8333) x 56.4o
13
12 July 2015
Trigonometry
Learning Objective To be able to use
trigonometry to find an unknown side in a
triangle.
14
Finding a side from a triangle
To find a missing side from a right-angled
triangle we need to know one angle and one other
side.
Note If
To leave x on its own we need to move the
13. It becomes a times when it moves.
Cos45 x 13 x
15
H
A
Cos 30
Cos 30 x 7 k 6.1 cm k
16
A
O
Tan 50
Tan 50 x 4 r 4.8 cm r
17
H
O
sin 25
Sin 25 x 12 k 5.1 cm k

18
Finding a side from a triangle
There are occasions when the unknown letter is on
the bottom of the fraction after substituting.
Move the u term to the other side. It becomes a
times when it moves.
Cos45 x u 13
To leave u on its own, move the cos 45 to other
side, it becomes a divide.
19
12 July 2015
Trigonometry
Learning Objective To be able to use
trigonometry to find an unknown side when the
unknown letter is on the bottom of the fraction.
When the unknown letter is on the bottom of the
fraction we can simply swap it with the trig (sin
A, cos A, or tan A) value.
20
H
Cos 30
x
A
x 5.8 cm
H
sin 25
O
m
m 18.9 cm
21
12 July 2015
Trigonometry
Learning Objective To be able to use
trigonometry to find unknown sides and unknown
angles in a triangle.
22
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