SS1 Third Term Further Mathematics Lesson Note – Trigonometric Ratios and Identities

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WEEK 6

TOPIC:   TRIGONOMETRIC RATIOS AND IDENTITIES:

CONTENT:

• GRAPHS OF TRIGONOMETRIC RATIOS
• TRIGONOMETRIC EQUATION

GRAPHS OF TRIGONOMETRIC RATIOS

Above are the graphs of the six trigonometric functions: sine, cosine, tangent, cosecant, secant and cotangent.

In the unit circle, the value of the hypotenuse is r = 1 so that sin  = y and cos . In other words, as we progressed from geometrical figures to a situation in which there was just one input (one angle measure, instead of three sides and an angle) leading to one output (the value of the trig ratio). And this kind of relationship can be turned into a function.

Trigonometric functions like others have their graphical representation, which is of great importance to scientists. Thus, it is one of the basic knowledges required in mathematics. The sine, cosine and tangent can be represented graphically in either degrees or radians as units of measurements. Though degree is often used.

The methods applied in table of trigonometry curves are similar to that of quadratic graph.

Example 1: a. Copy and complete the table below for the relation y = 2 sin 3x – 1

X	0°	30°	60°	90°	120°	150°	180°
Y = 2sin3x -1	-1					1

 

1. Using a scale of 2cm to 30°on the x-axis and 1cm to 1 unit on the y- axis, draw the graph of y = 2sin3x – 1 for 0°≤ x ≤ 180°
2. On the same axes draw the graph of y =

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