Reciprocal Trigonometric Ratios


 
 
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Reciprocal Trigonometric Ratios

Reciprocal Trigonometric Ratios: These are the trigonometric ratios which are the reciprocal of the three ratios sin A, cos A and tan A. The ratios are cosec A, sec A and cot A are respectively, the reciprocals of the ratios sin A,cos A and tan A. For a right triangle ABC right angled at B we observe that

cosecant ;of;angle A=cosec; A=frac{1}{sine;of;angle A}=frac{hypotenuse}{side;opposite;to;angle;A}=frac{AC}{BC}

secant ;of ;angle A=sec;A=frac{1}{cosine;of;angle A}=frac{hypotenuse}{side;adjacent;to;angle;A}=frac{AC}{AB}

cotangent; of ;angle A=cot;A=frac{1}{tan;A}=frac{side;adjacent;to;angle;A}{side;opposite;to;angle;A}=frac{AB}{BC}

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Sample Questions
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Question : 1

In figure,  Delta ABC is right angled at C. If BC = 3cm, AC = 4cm, find the values of cosec A.

Right Option : D
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Question : 2

ABC is a right angled triangle.If AB = 21cm, BC= 20cm and CA  = 29cm and angle;A= theta. ;Find; 21;sec;theta -29;cos;theta..

Right Option : C
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Question : 3

If 3;sec; theta = 5 find the value of

frac{5;sin;theta-4;cot;theta}{5;sin;theta+4;cot;theta}

Right Option : B
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