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1. MB1008: Trigonometry
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Important Definitions
1. Trigonometry is defined as the study of relationships between the sides and angles of a triangle.
2. In a right triangle ABC, right-angled at B, the trigonometric ratios are defined as
side opposite to angle A
sin A ,
hypotenuse
side adjacent to angle A
cosA
hypotenuse
side opposite to angle A
tan A
side adjacent to angle A



1
cosec A ;
sin A
1
sec A ;
cos A
1
tan A ,
cot A
sin A
tan A ,
cos A
cos A
cot A
sin A





Important Facts
1. If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of
the angle can be easily determined.
2. The values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the
triangle, if the angle remains the same.

2. MB1008: Trigonometry
Quick Review
 1350+ Videos;
 Well-detailed solutions to 3500+ problems
 Practice assignments
Get FREE Help in Maths at www.mathbuster.in
 HOTS quizzes
 Self-assessment quizzes
 Model Test Papers
 Expert guidance by mathematicians
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24 x 7 x 365 Access
to high quality content to learn, practice and assess.
24 x 7 x 365 Question & Answer Forum
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students from across India and abroad.
© 2013 – 2018, ECPL, New Delhi. This document is part of the MathBuster online education program. All intellectual rights associated to this document directly or indirectly are
owned by ECPL and any reproduction, derivation or distribution of this document in original or modified in full or parts, either in manual or electronic form is prohibited unless a
written approval is obtained. This document has been downloaded from www.mathbuster.in for personal and non-commercial use. For any queries, contact math@elipsis.in
2
3. The values of trigonometric ratios for angles 0 ,30 ,45 ,60 and 90    
are given as:
A 0 30 45 60 90
1 1 3
sin A 0 1
2 22
3 1 1
cos A 1 0
2 22
1
tan A 0 1 3 Not defined
3
2
cosec A Not defined 2 2 1
3
2
sec A 1 2 2 Not defined
3
1
cot A Not defined 3 1 0
3
     
4. The value ofsin AorcosA never exceeds 1, whereas the value ofsecA orcosecA is always greater
than or equal to 1.
 
 
sin 90 A cosA,
cos 90 A sin A;
 
 


 
 
tan 90 A cot A,
cot 90 tan A;A
 
 


 
 
sec 90 A cosec A,
cosec 90 A sec A.
 
 


5. 2 2
sin A cos A 1, 
6. 2 2
sec A tan A 1 for0 A 90 ,    
7. 2 2
cosec A 1 cot A for 0 <A 90º.  