Trigonometry

Introduction

     In Greek 'Trigonon' means a triangle. 'Metron' means a measure. The combination of these two words gives us the word 'Trigonometry'. Trigonometry is the branch of mathematics that deals with the relations between the sides and angles of triangles. In our study we will deal with the right angled triangles only.

Trigonometry

     (i) Sin q means a particular ratio. It is not sin multiplied by q.

     (ii) For trigonometrical ratios, short form T-ratios will be used.

     (iii) In right angled triangles T-ratios are obtained only for acute angles.

     (iv) T-ratios depend on only the magnitude of the angles and not on the size of the triangle.

Trigonometrical Ratios of Standard Angles

     0^o, 30^o, 45^o, 60^o and 90^o are called standard angles.

     These angles are called standard angles because it is possible to obtain simple mathematical ratios for these angles.

Trigonometric Equation

A trigonometric equation is an equation involving the trigonometric functions of unknown angles.

Example; sin x = 1/2.

Solving Trigonometric Equations

               Solution of trigonometric equation is value of the unknown angle

that satisfies the equation.

Summary

     1. Sine of Angle = (Apposite side / Hypotenuse)

     2. Cosine of Angle = (Adjacent side / Hypotenuse)

     3. Tangent of Angle = (Opposite side / Adjacent side)

     4. sine of an angle = cosine of its complement. If sin A = cos B, then A + B = 90^o.

     5. sin 0^o = 0, cos 0^o = 1, tan 0^o = 0

     6. sin 90^o = 1 cos 90^o = 0