Download Trigonometry - Minute Maths

WELCOME
Here you will learn how to:
 Identify certain parts of a right-angled triangle (hypotenuse, adjacent and
opposite sides)
 Recognise that the ratio of matching sides in similar right-angled triangles is
constant for equal sides
 Define the sine, cosine and tangent ratios for angles in right-angled triangles.
 Use a calculator to find trigonometric ratios in right-angled triangles, and to find
an angle, given the trigonometric ratio of the angle.
 Select and use appropriate trigonometric ratios in the right-angled triangles to
find unknown sides and angles.
 Learn about bearings and how to use a compass rose
NAMING SIDES OF A RIGHT-ANGLED TRIANGLE
In a right-angled triangle there are specific names of each of the sides, these
names include: Hypotenuse, adjacent and opposite. The hypotenuse is the
longest side of the right-angled triangle or opposite the right angle. In the triangle
ABC (below), if you stand at angle A, the side BC is the opposite side to you and
the side AB is the Adjacent side to you.
TRIGONOMETRIC RATIOS
The trigonometric ratios are the two sides of a right-angled triangle. The trigonometric
ratios – Sine, Cosine and tangent – are the most often used. (Note: the Greek
letter “theta”, is often used to represent the measure of an angle in degrees)
Theta
TRIGONOMETRIC RATIOS
If you are finding it difficult remembering the definitions, just remember SOH, CAH,
TOA.
USING THE CALCULATOR
When finding the trigonometric ratios of angles a calculator can be used. The order in
which keys are used depends on the type/model of a calculator. In this case we
will be using a casio fx-82AU PLUS (scientific calculator).
In trigonometry angles are usually measured In degrees, minutes and seconds. Key
relationships are depicted below.
An angle of 107’ 35’15’’ is an obtuse angle of 107 degrees, 35 minutes and 15
seconds. When transferred into degrees it will be 109’ because the minutes is
past 30 (halfway).
USING THE CALCULATOR
To enter angle sizes that has to do with degree and minutes into a calculator, use the
(degrees-minutes-seconds) key.
FINDING ANGLES WITH CALCULATOR
When given the scenario, sin A = 0.57, then angle A can be solved by using the
inverse Sin function on the calculator. The inverse sin function is activated by
pressing,
For example:
FINDING THE LENGTH OF A SIDE
Trigonometric ratios can be used to find the length of the side in a right-angled
triangle. There are five steps in finding the length these steps include:
Step 1: locate and mark the hypotenuse (H), opposite (0) and adjacent (A) sides of
the triangle.
Step 2: Decide whether sin, cos or tan should be used
Step 3: write the equation
Step 4: make the variable the subject
Step 5: use your calculator to evaluate the answer
Step 2
Step 3
Step 1
Step 4
Step 5
FINDING AN ANGLE
Similar to finding the length of a side, when finding the angle there are four main
rules that you must abide by.
Step 1: locate and mark in the hypotenuse (H), opposite (O) and adjacent (A) sides.
Step 2: Decide whether sin, cos or tan should be used.
Step 3: write an equation using the correct ratio.
Step 4: Use a calculator to evaluate the angle.
ANGLES OF ELEVATION AND DEPRESSION
The angle of elevation of an object when seen by an observer is the angle between
the horizontal and the line of sight.
ANGLES OF ELEVATION AND DEPRESSION
Similar to the angle of elevation, the angle of depression is when the object is below
the level of the observer. Therefore the angle between the horizontal and the
observer’s line of sight.
COMPASS BEARINGS
Compass bearings are those that use angles from 0’ to 90’ in order to show the
amount of turning from north (N) or south (S).
Important points:
•
North representing 0’ or 360’
•
East representing 90’
•
South representing 180’
•
West representing 270’
COMPASS BEARINGS
Also playing a key part in compass bearings is the Compass rose. A compass rose is a
diagram that shows north, east, south and west.
BIBLIOGRAPHY
•
http://web2.warillah.schools.nsw.edu.au/text_books/maths/New_Century_9/chapter06.pdf
•
http://www.mathsonline.com.au/
•
http://www.mathsisfun.com/algebra/trigonometry.html
•
http://www.sosmath.com/trig/trig.html
•
http://www.mathsteacher.com.au/year7/ch08_angles/07_bear/bearing.htm
•
http://mathworld.wolfram.com/Trigonometry.html
•
http://www.mathopenref.com/triginverse.html
•
http://www.mathwarehouse.com/trigonometry/inverse-sine-cosine-tangent/
•
http://dictionary.reference.com/