Reciprocal Trigonometric Ratios


 
 
Concept Explanation
 

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

If 13;sin ; theta = 12 Find the value of

large frac{13; cos;theta-12;cot;theta}{13;cos;theta+12;cot;theta}

Right Option : C
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Question : 2

Find the value of sec;theta+ ;2tan;theta when it is given that

cos; theta = frac{3}{5}

Right Option : B
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Question : 3

Express the trigonometric ratio tan A in terms of cot A.

Right Option : C
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Explanation
 
 
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