Download GM1-7-TrigBasics

GM1-7-TrigBasics.docx
TRIGONOMETRY
Watch the Higher GCSE Maths videoclip called: Trigonometry
Trigonometry is the branch of mathematics that looks at the relationships
between the sides and angles of triangles.
We are going to start looking at the basics which is the trigonometry linked to
RIGHT-ANGLED triangles and the three ratios or quotients called sine, cosine
and tangent.
Naming the Sides
The longest side in any triangle is called the Hypotenuse.
In right-angled triangles it is always opposite the right angle.
The other two sides are the one Opposite the other angle quoted or being found
and the one Adjacent (next to) this angle.
Examples:
Hyp
Adj
Opp
Adj
x
y
Opp
Hyp
The Ratios
The acronym
SOH – CAH – TOA
Sin x = Opp
Hyp
is used to help you remember that…
Cos x = Adj
Hyp
Tan x = Opp
Adj
These can be put into formulae triangles to use whether you are trying to find a
missing angle or a missing side…
S
O
x
H
C
A
x
H
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T
O
x
A
GM1-7-TrigBasics.docx
Finding Missing Sides
Look at the right angle and find the hypotenuse – label this side with an H.
Look at the other angle you have been given – label the side opposite it with an
O and label the last side with an A.
Which side have you got to find? Which side do you already know?
The two letters answering these questions will both appear in the ratio you need
to use.
In both of the examples below, find the length of the VERTICAL side.
E.g. 1:
A
72°
H
9cm
E.g. 2:
H
23°
O
O
12cm
A
I have to find the Adjacent side.
I know the Hypotenuse is 9cm.
A & H appear in CAH.
The angle is 72°.
I have to find the Opposite side.
I know the Adjacent is 12cm.
O & A appear in TOA.
The angle is 23°.
I want to find A.
When I cover it in the formula
triangle, I can see to find it, I
have to multiply C by H. So…
A = cos 72° x 9
A = 0.309017 x 9 = 2.78cm (to 3sf)
I want to find O.
When I cover it in the formula
triangle, I can see to find it, I
have to multiply T by A. So…
O = tan 23° x 12
O = 0.424475 x 12 = 5.09cm (to 3 sf)
Task: Find the lengths (to 3 s.f.) of x and y in this triangle.
3.5cm
X = ………………………cm
x
Y
Y = ………………………cm
37°
Save and complete the worksheet called: TrigS-S2.xlsx
Work through the MyMaths Lesson and online HW task: Trig Missing Sides
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GM1-7-TrigBasics.docx
Finding Missing Angles
Look at the right angle and find the hypotenuse – label this side with an H.
Look at the angle you have been asked to find and use it to label the side
opposite it with an O, and then label the last side with an A.
Which two sides do you know? Use their letters to find which ratio to use.
Once you have calculated the value of their trig ratio, use the inverse trig ratio
button to get back to the angle.
E.g. 1:
4.3cm
A
x
E.g. 2:
5.4cm
O
12.6m
H
x
H
6.3m
O
A
I know the lengths of the
Opposite and Adjacent sides.
O & A appear in TOA.
I know the lengths of the
Opposite and Hypotenuse sides.
O & H appear in SOH.
I want to find Tan x.
When I cover it in the formula
triangle, I can see to find it, I
have to divide O by A. So…
Tan x = 5.4 ÷ 4.3
Tan x = 1.255814
Inv Tan of 1.255814  x = 51.5°
I want to find Sin x.
When I cover it in the formula
triangle, I can see to find it, I
have to divide O by H. So…
Sin x = 6.3 ÷ 12.6
Sin x = 0.5
Sin-1 of 0.5  x = 30°
Tasks:
Calculate (to 1 d.p.) the size of angle x.
11m
x
7m
x = ……………°
Save and complete the worksheets called: TrigA-S2.xlsx
Work through the MyMaths Lesson and online HW task: Trig Missing Angles
Work through the MyMaths Lesson and online HW task: Trig Angles of Elevation
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