How to solve Trignometry Functions

Here Is one of the best topic of MATHEMATICS which allows us to find out

  • The heights of Buildings, towers, skyscraper sand trees, and mountain etc.
  • the elevation angle of top of any building with the horizon.
  • trigonometry allows us to project any thing from a certain distance​ and certain angle to attain maximum distance..
  • Best thing for Trigonometry I can say these progress​ what we are seeing around us couldn’t be possible without Trigonometry.

Trigonometry functions and their basics

now I’m going to explain the basic concepts of trigonometry
there are six Trigonometry functions exist 

sin ,  cosine ( cos ) , tangent ( tan ) , cotangent ( cot ) , sec , Cosec.

these functions are having different values around the axis with angles.

Trigonometry functions

so you can observe from the image all the different values of trigonometry​ functions  varies for sin and cos from 0 to 1 as angle varies from 0° to 90°.
but for other functions it is from 0 or 1 to 1 or undefined values.

for better understanding of trigonometry functions how they behave on Cartesian plane check this image out :-

Cartesian coordinates

from the above image it is clearly shown that for 1st quadrant all the functions are possessing positive values as we can see in above table and for 2nd, 3rd and 4th quadrant is (Sin, cosec), (tan, cot), and (cos, sec) are positive respectively and rest are negative in particular quadrants.

i.e. :-
sin90° = 1 but
sin 270° = ౼1
the reason is
sin 270° = sin ( 180° + 90°)
sin 270° = sin(౼ 90°)
sin 270°= ౼1
because up to 180° sin will remain positive after that it becomes negative.

From above table this doesn’t mean that Trigonometry functions have only values from 0° to 90° rather these functions have from 0° to up to whichever degree you can assume.


In any right angle triangle there is one base and perpendicular and a hypotenuse i.e.
briefly you can observe in following image:-

Trig Ratio

from this image we can find any of the Trigonometry ratio or angle with the help of three sides of any right angle triangle.
If we don’t know any of the side of triangle then we can find out by Pythagoras Formula i.e.

 H² = B² + P²

let H = 5 and B = 3 then P = ?q
by relationship 
5² = 3² + P² 
25 = 9 + P²
P² = 16
P = 4

Also read:

  • Interrelation of Trigonometry functions:-

sin∅ = 1/ cosec∅
cos ∅ = 1/ sec∅
tan∅ = 1/ cot∅

and vice verse.

tan∅ = sin∅/ cos∅
cot∅ =cos∅ / sin∅
some Trigonometry Identities which are much useful to solve problems are

sin²∅ + cos²∅ = 1
1+ cot²∅ = cosec²∅
tan²∅ + 1 = sec²∅

I hope this tutorial about Trigonometry has been proved very useful for you and now it’s over to you, If you want here to add something more which I’m missing do let me know, I’ll be pleased to hear from you.

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About the Author: Faizan

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