**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, 30, 45, 60 and 90**. 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.**

**(i)**

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

sin 0

sin 30

sin 45

sin 60

sin 90

**Note down the pattern from sin 0 to sin 90:**

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

Now, we will fill all the **cos values**.

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

**sin 0 = cos 90**

**sin 30 = cos 60**

**sin 45 = cos 45**

**sin60 = cos 30**

**sin 90 = cos 0**

Hence, all the **cos values** can be filled now.

We know that **tan = (sin )/(cos )**

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

tan 0 = sin 0 / cos 0 = 0/1 = 0

tan 30 = sin 30 / cos 30

tan 45 = sin 45 / cos 45

tan 60 = sin 60 / cos 60

tan 90 = sin 90 / cos 90 = 1/0 which is **NOT DEFINED**

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

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

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

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Posted in : NCERT Solutions, Trigonometry

Tags : 50 responses

cn u give values for 360 degrees

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)

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

Very helpful tip..

Can u give values for 180 & 270

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?

good thank you

very useful during exams.

Thank You.

easy way to learn trignometry table

I want to learn Math

This was totally useful for me....im studying 10th grade and this was helpful to me 😉

How Sin 0 =0 ,can you find it.

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...

the method given by you is quite easy...Thanks

thanx

I am preparing for NDA ,it helped me a lot

TANX A LOT

very helpful for student's

thanX

Thnku soo much...i was struglng frm a long time to learn these values...

It's really wonderful! Very useful....

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

awesome dude ...

Square root of 2/4 will be root2/2 not 1/root2

It is one and the same thing. You just remove square root from the denominator.

2/4 is 1/2 and under root 1/2 is 1 by under root 2

What is the value of cosh45

Thanx it is very useful!

ye values aayi kha se ?

ye values aayi kha se ? inka kya derivation h ?

Very nice

Helpful

all table sin cos tan etc

it is really very useful nice..☺☺

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

Thanks. It was really helpful.

What is the use of 0° value in Trigonometric Sums ?

You mast be come

hey guys this is really usefull i think the person that have any problem ......can be helped by this website

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

Very easy to learn. It's just awesome !!!!

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

and sin-(0.3 degrees)

Why should we calculate with sqrt 0/4, sqrt 1/4. What's the logic behind this?

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.

It is very useful and very helpful tnx

This trick is very useful and easy to learn t ratios angle values

Amazingly Helpful - Thanks! Memorised in 5 minutes.

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

THANK YOU VERY MUCH