Like us!

Have a Look!

WhatsApp Message

Share Link

Reciprocal Trigonometric Ratios

Introduction to Trigonometry I - Concepts

Identifying Hypotenuses In A Right Triangle

Identifying Adjacent Side To An Angle

Identifying Opposite Side To An Angle

Trigonometric Ratios

Reciprocal Trigonometric Ratios

Trigonometric ratios for 30 degrees

Trigonometric ratios for 45 degrees

Trigonometric ratios for 60 degrees

Trigonometric ratios for 90 degrees

Simplifying Trigonometric Expressions

Class - RRB Technician Grade I Signal Subjects

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

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

Illustration: Simplify the expression

$cot; Aleft ( frac{1}{cosec A} right )+ sec;A- left ( frac{1}{sec; A} right )$

Solution: To simplify the expression we will convert the ratios in terms of sin and cos.

$cot; Aleft ( frac{1}{cosec A} right )+ sec;A- left ( frac{1}{sec; A} right )$

$=frac{cos; A}{sin;A}left (sin ;A right )+ frac{1}{cos;A}- cos;A$

$=cos; A+ frac{1}{cos;A}- cos;A=frac{1}{cos;A}= sec;A$

Illustration: If $cosTheta =frac {p}{q},$ find the value of $cosecTheta .$

Solution:

We know $cosTheta =frac {base}{hypotenuse}$

We draw a right triangle, with right angle at C and having base BC = pk and hypotenuse BA = qk.

By the pythagorean theorem

$AB^2=BC^2+AC^2$

$Rightarrow$ $(qk)^2=(pk)^2+AC^2$

$Rightarrow$ $AC^2=(qk)^2-(pk)^2 =k^2(q^2-p^2)$

$Rightarrow$ $AC=k sqrt {q^2-p^2}: : : : : : [therefore AC>0]$

Thus, $cosecTheta =frac {hypotenuse}{perpendicular }=frac {qk}{ksqrt {q^2-p^2}}=frac {q}{sqrt {q^2-p^2}}$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

If $13;sin ; theta = 12$ Find the value of $large frac{13; cos;theta-12;cot;theta}{13;cos;theta+12;cot;theta}$
A. $dpi{110}frac{9}{13}$	B. $dpi{110}frac{5}{13}$	C. 0	D. None of these
Right Option : C
View Explanation

Question : 2

Express the trigonometric ratio tan A in terms of cot A.
A. $frac {1}{sqrt {1+2cot^2A}}$	B. $frac {1}{sqrt {1-cot^2A}}$	C. $frac {1}{cotA}$	D. None of these
Right Option : C
View Explanation

Question : 3

ABC is a right angled triangle.If AB = 21cm, BC= 20cm and CA = 29cm and $angle;A= theta. ;Find; 21;sec;theta -29;cos;theta.$ .
A. 5	B. 6	C. 8	D. 7
Right Option : C
View Explanation

Students / Parents Reviews [20]

Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.

Manish Kumar

10th

Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.

Om Umang

10th

A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre f...

Archit Segal

7th

I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying

Yatharthi Sharma

10th

Abhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.

Barkha Arora

10th

Third consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...

Ayan Ghosh

8th

Abhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary ...