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 :).
humza says
cn u give values for 360 degrees
Jashan says
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)
Xerus says
Can you give value for any degrees?
Like 234 degree, 156 degree etc.
Jashan says
@Xerus Manually there is no easy technique to find value of 234 degrees or 156 degrees. Technology can be used to find these values.
hafizmuzamil says
can u give me valuve of cosec 370
Raushan Yadav says
Super excited😁🤗😍😝
X square +7×10 = 0
T says
Sir you are great
Bhargav says
8.3666
Tobi says
The values for 360 are the same exact values for 0.
Sin 0 = sin 360
Tan 0 = tan 360, etc.
Sug says
Trigonometry is about right angled triangles which is 90 degree if u r saying 360 then it means a circle.
sabin says
It helped me alot thank u so much
Goutham says
I want sin 70 sin50 cos80
shouriyo says
nope
mariya says
sin(a + b) = sin a * cos b + cos a * sin b
Arjun S Chirackal says
I was struggling for a long time to learn the trignometrical values.This information was very helpful.Very easy method
Tanaya says
Correct
Sofi Lubna says
This was very helpful
Arjun says
Very helpful tip..
Asunain says
Value
Saumesh Kadam says
Can u give values for 180 & 270
Asmit says
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?
Dear HRS says
I guess you know that Tan (x)= perpendicular/base, and any triangle can only have 180* as total sum of internal angles, so we have 90*+90*+0*=180*, one of the 90* is of the right angle and other is of side named as x, so the third side has no magnitude and this triangle looks like this |_|
as the hypotneus has became parallel to perpendicular value for tan (x)= undefined, as this right-angled triangle is not possible.
Dear HRS says
Here, perpendicular is the opposite side from angle x and base is adjacent side from angle x, please note: we don’t take hypotenuse as adjacent or perpendicular. Angle x is one of the 2 angles, which are not 90*.
spark says
there is no such thing as tan90 as you can’t take trigonometric values of a triangle from the right angle.
danny says
Because Tan 90 would mean both Theta and the right angle are 90 degrees and therefore the third angle would be 0 degrees which isn’t possible. Also, Sine & Cosine I think about more having to do with circles. And at 90 degrees, inside a circle, the Y axis value in a unit circle is 1 and the x axis value in a unit circle is 0 and any fraction where the denominator is zero is undefined
JR BISWAL says
Tan90 is undefined because its value is infinite (tan90=sin90/cos90=1/0) Anything divided by 0 gives the infinite value. Also it can become clear if you look at the tan’s graph, it goes on increasing at 90 and -90 degrees. Hence its value is undefined at 90°.
saurabh says
good thank you
murtaza says
very useful during exams.
Thank You.
anany pandey says
easy way to learn trignometry table
Arman says
I want to learn Math
Debbie says
Okay 😒
Jashan says
Did you understand the article?
Ajitesh sharan says
This was totally useful for me….im studying 10th grade and this was helpful to me 😉
Mokshith says
Yes it’s true it’s very helpful to me ..
I’m 9 grade Mokshith in Tirupati AP INDIA
Sanjaya kumar sahoo says
How Sin 0 =0 ,can you find it.
Manish bihari says
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…
roshan kumar says
the method given by you is quite easy…Thanks
avadhut says
thanx
Rajat Pathania says
I am preparing for NDA ,it helped me a lot
A.y Balbaya says
TANX A LOT
Myana Shravani says
very helpful for student’s
amanshrivastava says
thanX
Shah saleeqa says
Thnku soo much…i was struglng frm a long time to learn these values…
Destiny Parker says
It’s really wonderful! Very useful….
Gyalbo Tamang says
i would like to repeat all trigonometry Formula but i doesn’t remember please send me all formula in my given above Email id..
RAMI REDDY DONDAPATI says
A VERY GOOD DIRECTIVE OM
N TRIGONOMETRIC VALUES
obed ningshen says
awesome dude …
Ginseng says
Square root of 2/4 will be root2/2 not 1/root2
Jashan says
It is one and the same thing. You just remove square root from the denominator.
Rishabh Singh says
2/4 is 1/2 and under root 1/2 is 1 by under root 2
some8thgrader says
exactly
Kuldeep choudhary says
What is the value of cosh45
Jyotiraditya Dash says
Thanx it is very useful!
shyam singh says
ye values aayi kha se ?
shyam singh says
ye values aayi kha se ? inka kya derivation h ?
Aju says
Very nice
abdul razzaq says
Helpful
Akash ghare says
all table sin cos tan etc
samiksha says
it is really very useful nice..☺☺
Lavanya says
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
Sandhya says
Thanks. It was really helpful.
Hunny Sharma says
What is the use of 0° value in Trigonometric Sums ?
Sandeep sharma says
You mast be come
ajay says
hey guys this is really usefull i think the person that have any problem ……can be helped by this website
ajay says
great great great great great great great great great ………………………………..keep doing this types of works pls
Arush Kumar says
Very easy to learn. It’s just awesome !!!!
jalla ramesh says
how to calculation of some fractional numbers like sin(0.30 or 0.526889 or 17 degrees) and with simple method
jalla ramesh says
and sin-(0.3 degrees)
Lara says
Why should we calculate with sqrt 0/4, sqrt 1/4. What’s the logic behind this?
Lara says
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.
Mohnish Singh says
It is very useful and very helpful tnx
Raj Patel says
This trick is very useful and easy to learn t ratios angle values
Jaime says
Amazingly Helpful – Thanks! Memorised in 5 minutes.
Jeremi Pieczka says
This page definitely has all the information I wanted about this subject and didn’t know who to ask.
Satendrasachin says
THANK YOU VERY MUCH
umang aggarwal says
it is very helpful to me.
Asad Ali Naseer says
very good thnk u
Rockin rooster says
Thanks a lot
It was very useful for my studies
sharma kuldeep says
thku so so much I love uu
Anj says
Thank you 😊😇
dhruv says
can u give the value tan 180
Dheeraj yadav says
Sin 30 =1/2 proved
Dheeraj yadav says
Sin 0= 0 provad thish strachar solved
I dont know please reply me
Kishan Rathod says
This is very nice trick i was trying to remember since many years but i learned through it in 5 mins
Sadaf says
That’s fantastic😌♥
Matthew Jones says
Thank you so much!
Tushar says
its amazing trick to remember these values
Imran says
Its amazing way find the value.. thanku so much
Shravani says
Thanks for this info… But I already knew the trick as one of my teacher told me😊😝
Laprince says
Incredible technique!
Govind kumar says
plz tel me how to comeing value of
Root 1/4 plz tel me
Piyush chaudhari says
Please define each part of sine and cos function position.(mean 0 to π/2, π/2 to π, π to 3π/2, 3π/2 to 2π which condition change function and which condition positive/nahative.)
Rani says
Thanks a lot
Kshitij thool says
Thank you very much this is most simple and elegant way to memorize.
Values of Trigonometric ratios for 0, 30, 45, 60 and 90 degrees.
Thanks Again.
gyanprakash choudhary says
tan 270 value define
Aastha says
Nice and very easy trick
Thanks a lot
travis says
This is a great and easy way to remember basic trig values. Thank you
Ali khan says
I think whole root of 2/4 is root 2/2. But u gave 1/root 2
I think it is not satisfy for sin 45.
Er. Atif Ahmad says
Good job
Too easy and very helpful.
Keep it up.
Laiba khan says
How can we find sec value 🤔
Laiba khan says
Sorry sorry now I have done sec value ☺sorry again!
sachin says
Can you give cos70 degree value
Jashan says
@sachin Manually there is no easy technique to find value of cos 70 degrees. Technology can be used to find this value.
Marko says
You can do the calculations that “technology” does by hand. See the Taylor Series. for a numerical approach
I Hassan says
What is triangle of sin0
pachchi says
This article made it so simple…thanks lot
Yulia says
Thank you! It’s really easy to understand and remember it now.
NAGI says
For a beginner it is so easy and simple to proceed further.
Joe says
Beautiful! Thank you for a lovely explanation!
Abhay mishra says
What is the value of tan 15°
harliem.jones says
tan(15)= 0.2679491924
harliem.jones says
I am doing a math assessment based on sin0, cos0, tan0, sin90, cos90 and tan 90. I can not even tell you haw any videos I have watched and websites I have read. it would be a god send if you could explain this in words
Grade 10 is tricky 🙁
Naveen says
What is the value of sin 17degree ?
Tell ma fast …?
jack frost says
0.29237
M$#n@k&^y says
Thankuuu for this lovely explanation.
Thankuu so muchh✌👍
kusuma says
thank you so much
Arunachalam says
Hey guys I am in 9th grade, I don’t understand what trignimentry is but I know the 0,30,45,60,90 degrees of sin,cos, and tan I memorized for my competition. I hope your 3 blocks may help me in my 10th grade. Now my doubt is how to find it help me
Stelin says
I want to learn maths.