SS1 Third Term Mathematics Lesson Note – Trigonometry I

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WEEK 2

TOPIC: TRIGONOMETRY 1

CONTENT:

• (a) Basic Trigonometric Ratios – (i) sine (ii) cosine (iii) tangent with respect to right-angled triangles. (b) Trigonometric ratio of; – (i) Angle 30⁰ (ii) Angle 45⁰ (iii) Angle 60⁰.

Basic trigonometric ratios (i) Sine  (ii) Cosine  (iii) Tangent with respect to right-angled triangles.

These trigonometric ratios are applicable to right – angled triangle. A right – angle triangle is 90⁰. Thus the remaining two angles add up to 90⁰ since every triangle contains two right angles.

In ∆ABC, B + C = 90⁰.

Such angles whose sum is 90⁰ are said to be complementary angles. While capital letter are used for angles, small (lower case) letters are used for sides. Notice that the side opposite A is labelled a, the one opposite B is labelled b etc.

The side opposite the right angle is called the hypotenuse. Every right – angled triangle obeys the Pythagoras theorem. This theorem states that the square of the hypotenuse of any right angled triangle is equal to the sum of the square of the other two sides.                                                                                         Thus in the above triangle,  a²=b²+c²

Apply Pythagoras theorem to the right – angled triangles below to find the lettered sides.

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