Basically, trigonometry is divided into 2 different levels of study ie Basic Trigonometry for PMR and Advanced Trigonometry for SPM level. Basic level will cover certain areas such as Sine, Cosine and Tangent of which the degree for each angle shall be less than 90°. On the other hand, students will be introduced to Sec, Cosec and Cot with the total degree of more than 90° in the following level.

Now let us look at how basic trigonometry works.

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**A Sin X = B** —-> **Sin X = B/A** —-> **X = Inverse Sin (B/A)**

**EXAMPLE 1**

Since Sin 30° = 0.5, as such 2 Sin 30° shall be calculated as 2 (0.5) = 1

**EXAMPLE 2**

If 2 Cos X = 1.7321

Cos X = 1.7321/2 = 0.8661

X = Inverse Cos 0.8661 = 30°

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**A Sin X + A Cos Y** —-> **A (Sin X + Cos Y)**

**EXAMPLE 3**

4 Sin 30° – 2 Cos 60° = 4(0.5) – 2(0.5) = 2 – 1 = 1

or

2( 2 Sin 30° – Cos 60°) = 2( 2(0.5) – 0.5 ) = 2(1 – 0.5) = 2(0.5) = 1

**EXAMPLE 4**

Find the value of M when 6 Sin 40° + 3 Cos M = 6

6 (0.6428) + 3 Cos M = 6

3.8568 + 3 Cos M = 6

3 Cos M = 6 – 3.8568 = 2.1432

Cos M = 2.1432/3 = 0.7144

M = Inverse Cos 0.7144 = 44.41° or 315.59° *****

or

3( 2 Sin 40° + Cos M ) = 6

2 Sin 40° + Cos M = 6/3 = 2

Cos M = 1 – 2 Sin 40° = 2 – 2(0.6428) = 2 – 1.2856 = 0.7144

M = Inverse Cos 0.7144 = 44.41° or 315.59° *****

***** refer to the diagram below

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As we have learnt from Polygons in Form 3 Maths, an individual angle may go beyond 90°. Due to this nature, we can safely say that each angle may vary from 0° up to 360° and anything more than that shall come in a repeated sequence accordingly; for example 450° is the same with 450° – 360° = 90° and so on. Now observe the diagram below that covers the range between 0° up to 360° which is defined under 4 different segment ( 360°/90° = 4) that shall be known as quadrant.

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