# 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.

(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.

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.

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.

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)

1. Arjun S Chirackal

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

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?

2. Ajitesh sharan

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

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...

3. Shah saleeqa

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

4. 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..

1. Jashan Post author

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

5. 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

6. ajay

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

7. ajay

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

1. jalla ramesh

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

8. 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.

9. Jeremi Pieczka