Introduction To Trigonometry Class 10 Notes Maths: Chapter 8

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Introduction Totrigonometry

If triangle ABC is right-angled at B and ∠BAC = θ, then with reference to the angle θ, we have Base = AB, Perpendicular = BC, and Hypotenuse = AC , and

$$sin\space\theta=\frac{Perpendicular}{{Hypotenuse}}:cos\space\theta=\frac{Base}{{Hypotenuse}}:\\tan\space\theta=\frac{Perpendicular}{{Base}}:cot\space\theta=\frac{Base}{{Hypotenuse}}:\\sec\space\theta=\frac{Hypotenuse}{{Base}}:coses\space\theta=\frac{Hypotenuse}{{Perpendicular}}$$

$$\frac{1}{{sin\space\theta}}\space cosec\space\theta ;sec\space\theta= \frac{1}{{cos\space\theta}} ;cot\space\theta= \frac{1}{{tan\space\theta}}$$

$$tan\space\theta= \frac{sin\space\theta}{{cos\space\theta}}\space and \space cot\space\theta=\frac{cos\space\theta}{{sin\space\theta}}$$

The trigonometric ratios for angles 0°, 30°, 45°, 60°, and 90° are given in the table below :

Identity / Ratio	0°	30°	45°	60°	90°
sin θ	0	1/2	1/√2	√3/2	1
cos θ	1	√3/2	1/√2	1/2	0
tan θ	0	1/√3	1	√3	∞
cosec θ	∞	2	√2	2/√3	1
sec θ	1	2/√3	√2	2	∞
cot θ	∞	√3	1	1/√3	0

if θ is an acute angle, then


sin (90°− θ)= cos θ ;	cos (90°− θ)= sin θ ;
tan (90°− θ)= cot θ ;	cot (90°− θ)= tan θ ;
sec (90°− θ)= cosec θ ;	cosec (90°− θ)= sec θ ;
sin (− θ)= − sin θ ;	cos (− θ)= cos θ ;
tan (− θ)= − tan θ ;	sec (− θ)= sec θ ;
cosec (− θ)= − cosec θ ;	cot (− θ)= − cot θ ;