In a right-angled triangle

MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

In a right-angled triangle, angle

\theta

is one of the acute angles. (i) Define

\sin\theta

and

\cos\theta

in terms of the sides of the triangle. (ii) Define

\tan\theta

in the same triangle. (iii) Using only the three definitions obtained in parts (i) and (ii), establish the relationship

\tan\theta = \dfrac{\sin\theta}{\cos\theta}

. (iv) Briefly explain why this relationship is valid for every acute angle

\theta

in such a triangle.