Figure — △ ABC
A B C D 30° 30° 60° 60° 2x 2x x x √3x
Side = 2x
Half-base = x
Height = √3x
Therefore — 30° ratios
Trigonometric values
sin 30°
12
cos 30°
√32
tan 30°
1√3
cosec 30°
2
sec 30°
2√3
cot 30°
√3
Figure — ∠AOB = 45°
O B A P Q α=45° x x x √2x
Given sides
OQ = PQ = x
OP = √2x
Therefore — 45° ratios
Trigonometric values
sin 45°
1√2
cos 45°
1√2
tan 45°
1
cosec 45°
√2
sec 45°
√2
cot 45°
1
Figure — △ ABC
A B C D 30° 30° 60° 60° 2x 2x x x √3x
AB = 2x (hyp.)
BD = x (adj.)
AD = √3x (opp.)
Therefore — 60° ratios
Trigonometric values
sin 60°
√32
cos 60°
12
tan 60°
√3
cosec 60°
2√3
sec 60°
2
cot 60°
1√3
Trigonometric Ratios — Special Angles
Summary table · 30° · 45° · 60°
Ratio
30°
45°
60°
30°
45°
60°
sin
12
1√2
√32
cosec
2
√2
2√3
cos
√32
1√2
12
sec
2√3
√2
2
tan
1√3
1
√3
cot
√3
1
1√3