JSS3 First Term Mathematics Lesson Note – Trigonometry

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WEEK 6

TOPIC: TRIGONOMETRY

CONTENT:

• Right angle triangle (Revision)
• Relationship between right angle triangles and trigonometric ratios.
• Sine, cosine and tangent of acute angles using tables.
• Applications of trigonometric ratios to finding distances and lengths.

Right Angled Triangle

A right angled triangle has one of its angles equal to 90^O. That is, if a triangle has one of its three angles equal to 90^O then it is a right angled triangle. A little square at the corner (angle) signifies that the angle is 90^O.

Right Angled Triangle and the Trigonometric Ratios

A trigonometric ratio is a ratio of the lengths of any two sides of a right – angled triangle. The longest side is called the Hypotenuse, the side facing the required angle is called the opposite and the last side is called the adjacent.

The three trigonometric ratios are Sine (sin), Cosine (cos) and Tangent (tan).

The figure below show triangle XYZ in various positions

Where H, A, O represent the Hypotenuse, Adjacent and Opposite respectively.

The sides of the triangles are as follows.

XZ, the hypotenuse, XY, the side opposite to and YZ, the side adjacent to

Using these abbreviations hyp, opp and adj, the Trigonometric ratios are given as:

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