Reciprocal Trigonometric Ratios


 
 
Concept Explanation
 

Reciprocal Trigonometric Ratios

Reciprocal Trignometric 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}

cot;A =frac{AB}{BC}=frac{frac{AB}{AC}}{frac{BC}{AC}}=frac{cos;A}{sin;A}

Illustration:  ABC is a right angled triangle. If AB = 21 cm, BC =  20 cm and CA  = 29 cm and large angle;A= theta. ;Find; cot;theta..

Solution: As per definition we know that

large cot;theta= frac{Adjacent; Side}{Opposite ;Side}=frac{AB}{BC} = frac{21}{20}

 

 

Sample Questions
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Question : 1

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 : 2

In figure,  Delta ABC is right angled at C. If BC = 3cm, AC = 4cm, find the values of 3 cot A + 2 tan A

Right Option : B
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Explanation
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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