Let’s see the angles in different Quadrants
- In Quadrant 1 , angles are from 0 to 90°
- In Quadrant 2 , angles are from 90 to 180°
- In Quadrant 3 , angles are from 180° to 270°
- In Quadrant 4 , angles are from 270 to 360°
To learn sign of sin, cos, tan in different quadrants,
we remember
A dd → S ugar → T o → C offee
Representing as a table
|
Quadrant I |
Quadrant II |
Quadrant III |
Quadrant IV |
|
|
sin |
+ |
+ |
– |
– |
|
cos |
+ |
– |
– |
– |
|
tan |
+ |
– |
+ |
– |
What about cot, sec, cosec?
We know that
tan = sin/cos
sec = 1/cos
cosec = 1/sin
cot = 1/tan
So,
-
In
1
st
quadrant
-
sin, cos both +ve.
tan = sin/cos = +/+ = +
cosec = 1/sin = 1/+ = +
sec = 1/cos = 1/+ = +
cot = 1/tan = 1/+ = +
-
In
2
nd
quadrant
-
sin is +ve, cos is –ve.
tan = sin/cos = +/– = –
cosec = 1/sin = 1/+ = +
sec = 1/cos = 1/– = –
cot = 1/tan = 1/– = –
-
In
3
rd
quadrant
-
sin is –ve, cos is –ve.
tan = sin/cos = –/– = +
cosec = 1/sin = 1/– = –
sec = 1/cos = 1/– = -
cot = 1/tan = 1/+ = +
-
In
4
th
quadrant
-
sin is –ve, cos is +ve.
tan = sin/cos = –/+ = –
cosec = 1/sin = 1/– = –
sec = 1/cos = 1/+ = +
cot = 1/tan = 1/– = –