Page 23 - 11-Math-9 Fundamentals of Trigonometry

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version: 1.1
half the hypotenuse.
Let c = 2 then b = 1

\ By Pythagoras theorem ,

\ a2 + b2 =c2
⇒ a2 =c2 - b2

= 4-1= 3
⇒ a =3

\ Using triangle of fig.3, with a = 3, , b = 1 and c = 2

sin 60= a= 3 ; csc 60= sin160= 2;
c2 sec 60= 3
cot 60= cos160= 2;
cos 60= b= 1 ; tan160= 1.
c2 3

tan 60= a= 3;
b

Example 3: Find the values of all the trigonometric functions of

(i) 420° (ii) -7π (iii) 19π
4 3

Solution: We know that q=+ 2kπ q , where k ∈ Z

(i) 420° = 60°+ 1(360°) (k= 1)

= 60°

∴ sin 420 =sin 60 = 3 ; csc 420 =2
2 3

cos=420 c=os 60 1 ; se=c 420 2
tan=420 2 co=t 420 1

t=an 60 3 ; 3

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