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Values of Trigonometric ratios for 0, 30, 45, 60 and 90 degrees

 

Values of Trigonometric ratios for 0, 30,45, 60 and 90 degrees

 

I have noticed that students cannot actually remember values of six trigonometric ratios (sin, cos, tan, cosec, sec and cot) for 0^\circ, 30^\circ, 45^\circ, 60^\circ and 90^\circ. These values are used very often and it is recommended from my point of view that student should be able to tell the values instantly when asked.

 

There is a proper method to memorize all of them. Lets go through it.

 

In this post our motive is to learn how to fill the table. Once, you learn to fill this table, you would be able to calculate any value in your mind.

 

How to memorize values of Trigonometric Ratios for 0, 30, 45, 60 and 90 degrees

 

(i)

Just memorize the values for sin 0^\circ, sin 30^\circ, sin 45^\circ, sin 60^\circ and sin 90^\circ. Even there is no need to try too hard to memorize them. There is an easy way to memorize them.

 

sin 0^\circ=\sqrt{\frac{0}{4}}=0

 

sin 30^\circ=\sqrt{\frac{1}{4}}=\frac{1}{2}

 

sin 45^\circ=\sqrt{\frac{2}{4}}=\frac{1}{\sqrt{2}}

 

sin 60^\circ=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}

 

sin 90^\circ=\sqrt{\frac{4}{4}}=1

 

Note down the pattern from sin 0^\circ to sin 90^\circ:

\sqrt{\frac{0}{4}},\sqrt{\frac{1}{4}}, \sqrt{\frac{2}{4}}, \sqrt{\frac{3}{4}}, \sqrt{\frac{4}{4}}

 

Hence, we can now fill all sin values in the table.

 

How to memorize values of Trigonometric Ratios for 0, 30, 45, 60 and 90 degrees

 

Now, we will fill all the cos values.

All the cos values are filled in opposite order starting from sin 0^\circ to sin 90^\circ. I mean to say that

 

sin 0^\circ = cos 90^\circ

 

sin 30^\circ = cos 60^\circ

 

sin 45^\circ = cos 45^\circ

 

sin60^\circ = cos 30^\circ

 

sin 90^\circ = cos 0^\circ

 

Hence, all the cos values can be filled now.

How to memorize values of Trigonometric Ratios for 0, 30, 45, 60 and 90 degrees

We know that tan \theta = (sin \theta)/(cos \theta)

Hence, all the tan values can be obtained from sin and cos values.

 

tan 0^\circ = sin 0^\circ / cos 0^\circ = 0/1 = 0

 

tan 30^\circ = sin 30^\circ / cos 30^\circ=\frac{1}{\sqrt{3}}

 

tan 45^\circ = sin 45^\circ / cos 45^\circ=1

 

tan 60^\circ = sin 60^\circ / cos 60^\circ=\sqrt{3}

 

tan 90^\circ = sin 90^\circ / cos 90^\circ = 1/0 which is NOT DEFINED

 

Similarly, we have sec \theta = 1/cos \theta, cot \theta = cos \theta / sin \theta and cosec \theta = 1/ sin \theta.

 

Hence, all the tan, sec, cosec and cot values can be filled now.

How to memorize values of Trigonometric Ratios for 0, 30, 45, 60 and 90 degrees

 

Now, try to derive these values in your mind :).


 


Posted in : NCERT Solutions, Trigonometry


Tags : 50 responses



50 thoughts on “Values of Trigonometric ratios for 0, 30, 45, 60 and 90 degrees


    1. Jashan Post author

      sin 360 degrees=sin(270+90)=-cos(90)=0
      cos 360 degrees=cos(270+90)=sin(90)=1
      tan 360 degrees=sin (360)/cos (360)=0/1=0
      cot 360 degrees= cos (360)/sin(360)=1/0 (Not defined)
      sec 360 degrees=1/(cos 360)=1
      cosec 360 degrees=1/sin(360)=1/0 (Not defined)

      Reply
  1. Arjun S Chirackal

    I was struggling for a long time to learn the trignometrical values.This information was very helpful.Very easy method

    Reply
    1. Asmit

      I don't understand one thing.
      I just started Trigonometry and I got that Tan=Opp/Adj
      But if you take a standard right triangle and try to calculate the tangent of the right angle(90) then the hypotenuse would be the opposite side but which side would we take as the adjacent the perpendicular or the base? Further more regardless of which side we take tangent of 90 degrees would still be defined so how can tan 90 not be defined?

      Reply
    1. Manish bihari

      Yu want to know values of sin0`.... In root 0/4=0
      sin30 in root 1/4=1/2
      sin45 in root 2/4=1/root 2
      sin60 in root 3/4=root 3/2
      sin90 in root 4/4=1
      now,yu try to do in yur mind...

      Reply
  2. Gyalbo Tamang

    i would like to repeat all trigonometry Formula but i doesn't remember please send me all formula in my given above Email id..

    Reply
  3. Lavanya

    It's an amazing trick . I was struggling hard to learn this but you made it very easy thanx a lot pls upload all maths formulas

    Reply
  4. ajay

    great great great great great great great great great ......................................keep doing this types of works pls

    Reply
    1. jalla ramesh

      how to calculation of some fractional numbers like sin(0.30 or 0.526889 or 17 degrees) and with simple method

      Reply
  5. Lara

    This process is known to me as I'm a teacher in maths. But logic I do not know. Which I need to explain to my students.

    Reply
  6. Jeremi Pieczka

    This page definitely has all the information I wanted about this subject and didn't know who to ask.

    Reply

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