untitled

angle

Ratio 0 $ 30 $ 45 $ 60 $ 90 $

sine 0

2

1

2

1

2

3 1

cosine 1

2

3

2

1

2

(^10)
tangent 0
3
(^113) undefined
cotangent undefined 3 1
3
1 0
secant 1
3
(^22) 2 undefined
cosecant undefined
2
(^12)
3
2 1
Observe : Easy method for remembering of the values of trigonometric ratios of
some fixed angles.
(i) If we divide the numbers 0 , 1 , 2 , 3 and 4 by 4 and take square root of the
quotients, we get the values of sin 0 $ofsin 30 $,sin 45 $,sin 60 $andsin 90 $
respectively.
(ii) If we divide the numbers 4 , 3 , 2 , 1 and 0 by 4 and take square root of
quotients, we get the values of cos 0 $,cos 30 $,cos 45 $,cos 60 $and cos 90 $
respectively.
(iii) If we divide the numbers 0 , 1 , 3 and 9 by 3 and take square root of quotients,
we get the values of tan 0 $, tan 30 $,tan 45 $ andtan 60 $, respectively (It is
noted that tan 90q is undefined).
(iv) If we divide the numbers 9 , 3 , 1 and 0 by 3 and take square root of quotients,
we get the values of cot 30 $,cot 45 $,cot 60 $,cot 90 $ respectively (It is noted
thatcot 0 $ is undefined).
Example 1. Find the values :
(a) $ $
$
n 45
1 n 45
1 n (^452)
2
2
ta
si
si



(b) cot 90 $˜tan 0 $˜sec 30 $˜cosec 60 $
(c) sin 60 $˜cos 30 $cos 60 $˜sin 30 $
(d) $ $
$
n 60
1 n 60
1 n (^602)
2
2
si
si
ta