Find Value of Sin and Cos using Fingers

Today I am going to share with you a special memory trick for trigonometry, mailed to me by Debasis Basak – a young Class IX follower of

By this method we can find out Sines and Cosines of different angles. It just requires your left hand. Let’s understand this trick step by step –

Step 1:-
First mark the angles of 0, 30, 45, 60, and 90 on little, ring, middle and pointer finger and thumb of your left hand.

Step 2:-
On the palm of your left hand write the equation √x /2

Find Value of Sin and Cos

Step 3:-
Suppose, you want to find Cos30. 

Fold the finger representing 30. i.e. ring finger of your left hand palm.  Count the numbers of fingers on the left of the ring finger. So since there are 3 fingers, x=3; put the value in the equation given in step 2

Step 4:-
Cos30 = √3/2

Finding Sine of the same angle is just a simple step away. Of the same left hand, if we count the fingers to the right of the folded finger, we will get value of sine.

Sin30 = √1 /2 = 1/2

Let’s take another example, sin60

60 is represented by pointer finger and there are 3 fingers to the right of this folded finger.

Hence, sin60 = √3/2

I appreciate the efforts of Debasis in sharing this trick with all of us. In case you want to share some quick calculation trick or technique, mail it to me at vineetpatawari [at] gmail [dot] com.

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Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

32 thoughts to “Find Value of Sin and Cos using Fingers”

  1. please… may may i know some other easy formula to calculate the trignometric values ….the above shared is boring and how i know from which side of hand to start counting for sine or cos…

  2. These all above given values are so simple n the better way is to learn them by heart rather than spoiling ur hands with ink . Wat’s tough is calculation of further sin and cos values.if u have any trick for it plz let me know

    1. which angles of sin and cosine are difficult to find. if you had written about them then i would have tried to answer your query. in absence i believe sin15 , sin 18 etc. must have troubled you. a simple thing is to write them as they occur, after all rest of the values can be looked up through the tables and nobody expects you to memorize them

    1. Hi Krishna,

      This is very common. Because of exam stress our mind stops working at optimal level. Meditation at your age might be difficult. Try joggin or some other activity for 30-40 mintues as stress buster during exam days.


    1. it works for sin 45 and cos 45 as well
      sin 45 = (sqrt(2)/2)*(sqrt(2)/sqrt(2)) = 2/2*sqrt(2) = 1/sqrt(2)
      cos 45 = (sqrt(2)/2)*(sqrt(2)/sqrt(2)) = 2/2*sqrt(2) = 1/sqrt(2)

  3. Hi friends i found new method by own to calculate square of numbers which ends with 1
    For ex. 31
    square of 3 is 9 and 2*3 is 6 and square of 1 = 961
    similarly 51
    square of 5 is 25 and 2*5 is 10,here 1 is passed to previous digit square of 1 = 2601
    i have also found for other no. also but again it is bit lengthy.

  4. it could be simple… it goes
    angle 0 30 45 60 90
    sin sq rt (0/4) sq rt (1/4) sq rt (2/4) sq rt (3/4) sq rt (4/4)
    cos (reverse the sequence)
    sq rt (4/4) sq rt (3/4) sq rt (2/4) sq rt (1/4) sq rt (0/4)
    tan sin 0/cos 0 sin 30/ cos 30… on
    cosec 1/sin 0 1/sin 30…….so on
    sec 1/cos 0 1/cos 30…… on
    cot 1/tan 0 1/tan 30…….so on

  5. Certainly a very good Idea; works perfect for at least sine and cosine functions;
    However, I didn’t found any glitch in it.
    equation is: x=sqrt(x)/2 and not sqrt(x/2).
    Perfectly fine for me.

  6. It is certainly a good idea. But there is a small glitch. Sin 30 is 1/2 while Cos 30 is (sqrt 3) /2. The sqrt applies only to 3 and not to 2.
    Similarly for 45, both sin and cos is 1 / (sqrt 2).
    Needs a bit of tweaking?

    1. no sir , there is no need of tweaking. in sin 30 as you said , when you bend the the ring fnger 30 degrees you know that cos 30 is sqrt 3 /2 for sin please see the fingers lefton the right side . it is 1 therefore sin30 is sqrt1/2 or 1/2

  7. ………………..amaxing……………..I appretiate U for making such efforts…………………………

  8. When you say bend the ring finger the left side has one finger left and on the right side there are 3 fingers. It works for 30 and 90 well but not for all.
    Though the efforts are nice

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