back to the time where we are pirates of the sea searching for gold.
have any gps here, so how can we find our position and location.
Trigonometry is made from two greek words , trigon, meaning triangles and metron, meaning measure.
trigonometry is the study of angles, ratios and sides of triangles.
We have a
triangle, we have three sides, three angles and that’s it.
Let’s get a feel of trigo by getting into a situation.
trigonometry -> the situation
are on a boat which is a few metres away
from a light house.
Now , what
if we want to find the distance of the boat from the light house ?
It is assumed
that the height of the light house is
What if we also
know the angle which light house makes from our boat ?
easily find the distance.
Do you know that the ratio of two sides of a right angled triangle is fixed if one of the angle is fixed ?
So, p/b = c
(a fixed no.)
above equation, we can easily find b, as p and c are known.
Now, as we are humans we can’t believe anything
So, we must
have a proof of this statement :
ratio of any two sides of a right angled triangle is fixed if one of the angle is fixed.
have a triangle ABC, where
AB = 2cm, AC = 4cm,
BC = √12 cm.
ACB = 30°.
If we just
double the length of AB and fix the angle to be 30°.
have to increase the lengths of AC and BC.
measuring AC, we have AB = 4cm and AC = 8 cm.
AB/AC = 4/8 = 1/2.
proved that if the angle is fixed , then the ratios of the lengths of any two
sides is a constant.
Now, for different angles, we have different constants.
have six different ratios.
that we have three sides of a triangle,
are : hypotenuse( the longest side) ,H
Now, we have
the following ratios :
Now for different angles we have different value of P/H .
trigonometry-> the naming
So, we can’t
just name it as anything.
We have to
name it in such a way that the name contains the angle so that no one get
We name it
as sine .
the above example, sine of 30 degree is 1/2.
Now it is
very boring and time taking to write sine of 30 , so we denote it as sin(30) =
for every ratio, we have a function , called trigonometric function which takes
angle as input and give the output as a constant.
are the names, formulae and abbreviations of these functions.
P/H sine sin
B/H cosine cos
H/P cosecant cosec
H/B secant sec
B/P cotangent cot
What we have
inverse of sine.
inverse of cosine.
inverse of tangent.
Also , sin/cos = p/h / b/h = p/b = tan
Now, we will
study some properties of these functions :
+ cos2x = 1.
+ 1 = sec2x.
1 + cot2x
To know the proof of them, just see the following post :
Here are solutions of trigonometry class 10 NCERT