TRIGONOMETRICAL IDENTITIES
cos (180 - θ )
- cos θ
sin (-θ)
- sin θ
tan (-θ)
- tan θ
cos 180
-1
sin 270
-1
cos 270
0
cos 90
0
sin 0
0
sin 180
0
tan 0
0
tan 180
0 since sin 180 = 0
cos 0
1
sec²θ - tan² θ
1
sin 90
1
sin² θ + cos² θ
1
sin²θ + cos²θ
1
cosec θ
1 / sin θ
sec θ
1/ cos θ
cot θ
1/tanθ =cosθ/sinθ
cos 45
1/√2
sin 45
1/√2
Area of a triangle without a right angle
A= ½ ab Sin C
Cosine Rule to find an angle
Cos C =(a² + b² - c²) /(2ab)
sin 30
Same as cos 60 = ¹/₂
sec 60
Same as cosec 30 = 2
sec 30
Same as cosec 60 = 2/ √3
sin 60
Same as sin 30 = √3/2
cos 30
Same as sin 60 = √3/2
cos 60
Same as sine 30 = 1/2
Sine Rule to find an angle
SinA/a = SinB/b = SinC/c
Sine Rule to find a side
a/sinA =b/sin B =c/sin C
sin (90 - θ)
cos θ
sec (90 - θ)
cosec θ
tan (90 - θ)
cot θ
cosec²θ + 1
cot² θ
1 + cosec ²θ
cot²θ
Cosine Rule to find a side
c² =a² + b² - 2abCos C
What is the sign of cos 135
negative
What is the sign of cos 240
negative
What is the sign of sin 240
negative
What is the sign of sin 330
negative
What is the sign of tan 150
negative
What is the sign of tan 315
negative
What is the sign of cos 320
positive
What is the sign of sin 150
positive
What is the sign of tan 225
positive
1 + tan²θ
sec ²θ
cosec (90 - θ)
sec θ
Which quadrant is 180 - θ
second quadrant
cos (90 - θ)
sin θ
tan θ
sinθ / cos θ
cot (90 - θ)
tan θ
Which quadrant is 180 + θ
third quadrant
tan 270
undefined since cos 270 = 0
tan 90
undefined since cos 90 = 0