NCERT Class 10th Introduction to Trigonometry

• The word ‘trigonometry’ is derived from the Greek words ‘tri’ (means Three)’ ‘gon’ (means sides) and ‘metron’ (means Measure). In fact, Trigonometry is the study of relationships between the sides and angles of a triangle.   

  

                                         

• Trigonometric ratios

        Ratio of the sides of a right triangle with respect to its acute angles are called trigonometric ratios of the angle.

        

        
The trigonometric ratios of the angle A in a right angle ∆ABC right angled at B are defined as follows:

        

 Note - The ratios cosec A, Sec A and cot A are respectively the reciprocals of the ratios sin A, cos A and tan A.

Trigonometric Ratios for complementary angles

Recall that two angles are said to be complementary if their sum equals to 90°

sin (90° – A)     = cos A
cos (90° – A)     = sin A
tan (90° – A)     = cot A
cot (90° – A)     = tan A
sec (90° – A)     = cosec A
cosec (90° – A) = sec A
Here (90° – A) is the complementary

angle of ∠A.

• Trigonometric Identities

An equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle involved.

(i)                   sin²θ + cos²θ     = 1               [for 0° ≤ θ ≤ 90°]

(ii)                sec²θ – tan²θ     = 1               [for 0° ≤ θ ≤ 90°]

(iii)             cosec²θ – cot²θ = 1               [for 0° < θ ≤ 90°]