TRIG

ONOMETRY

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I S R

OS

AL E

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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 1

Step 3

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 DEPRESSIONThe 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 DEPRESSIONSimilar 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.warilla-h.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/