Reciprocals of basic triginometric ratios — lesson. Mathematics CBSE, Class 10.

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Based on the three basic trigonometric ratios

$\sin$ ,

$\cos$ and

$\tan$ we will define its reciprocals.

Reciprocal Ratios:

Consider a right-angled triangle with a corresponding angle

$\theta$ .

The three basic trigonometric ratios are:

The table below depicts the relation of reciprocal ratios with the right-angled triangle.

*Name of the angle*	Sine	Cosine	Tangent
*Short form of the angle*	$\sin$	$\cos$	$\tan$
*Relationship*	$\sin \theta$ $=$ $\frac{\text{Opposite side}}{\text{Hypotenuse}}$	$\cos \theta$ $=$ $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$	$\tan \theta$ $=$ $\frac{\text{Opposite side}}{\text{Adjacent side}}$
*Name of the reciprocal angle*	Cosecant	Secant	Cotangent
*Short form of the angle*	$\text{cosec}$	$\sec$	$\cot$
*Measurements related to the right-angled triangle*
*Relationship*	$\text{cosec}\,\theta$ $=$ $\frac{\text{Hypotenuse}}{\text{Opposite side}}$	$\sec \theta$ $=$ $\frac{\text{Hypotenuse}}{\text{Adjacent side}}$	$\cot \theta$ $=$ $\frac{\text{Adjacent side}}{\text{Opposite side}}$
*Relation with the basic ratio*	$\text{cosec}\,\theta$ $=$ $\frac{1}{\sin \theta}$ or $\sin \theta$ $=$ $\frac{1}{\text{cosec}\,\theta}$	$\sec \theta$ $=$ $\frac{1}{\cos \theta}$ or $\cos \theta$ $=$ $\frac{1}{\sec \theta}$	$\cot \theta$ $=$ $\frac{1}{\tan \theta}$ or $\tan \theta$ $=$ $\frac{1}{\cot \theta}$