Signs of sin, cos, tan in different quadrants

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

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/– = –