Signs of sin, cos, tan in different quadrants

Last updated at April 16, 2024 by

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°

Angles in different quadrants.jpg

 

To learn sign of sin, cos, tan in different quadrants,

we remember

A dd → S ugar → T o → C offee

 

Signs of sin, cos, tan in different quadrants - Part 2

 

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/– = –

Transcript

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 Add Sugar To Coffee 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 1st quadrant - sin, cos both +ve. tan = sin/cos = +/+ = + cosec = 1/sin = 1/+ = + sec = 1/cos = 1/+ = + cot = 1/tan = 1/+ = + In 2nd quadrant - sin is +ve, cos is ve. tan = sin/cos = +/ = cosec = 1/sin = 1/+ = + sec = 1/cos = 1/ = cot = 1/tan = 1/ = In 3rd quadrant - sin is ve, cos is ve. tan = sin/cos = / = + cosec = 1/sin = 1/ = sec = 1/cos = 1/ = - cot = 1/tan = 1/+ = + In 4th quadrant - sin is ve, cos is +ve. tan = sin/cos = /+ = cosec = 1/sin = 1/ = sec = 1/cos = 1/+ = + cot = 1/tan = 1/ =

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.