INTRODUCTION - TRIGONOMETRY

Trigonometry means (triangle + measure)

Trigonometry is all about triangle measurement.

Base of trigonometry is depending on Pythagorean theorem. Pythagorean theorem is also known as Pythagoras theorem.

Pythagoras theorem –“In a right angle triangle the square of a long side is equal to sum of the square of the other two sides.”

Let we assume that adjacent=x, opposite=y and hypotenuse=z.

We right this theorem like as Z²=X² + Y²

With the help of this formula people can calculate hypotenuse, adjacent and opposite easily if one is missing.

Now we measure the Angle(θ)

Suppose in a right angle triangle, we assume an angle θ, then sine, cosine and tangent (special functions) help us.

Sine function; Sinθ =opposite/hypotenuse. 

Cosine function; Cosθ =adjacent/hypotenuse.

Tangent function; Tanθ =opposite/adjacent.

Some time we are very confused to these formulas.so we learn these formulas in a simple way.

That is O A O/H H A, so we learn like as –

Sinθ =O/H =opposite/hypotenuse.sss

Cosθ =A/H =adjacent/hypotenuse.

Tanθ =O/A =opposite/adjacent.

Similar to sine, cosine and tangent functions, there are three other trigonometry functions.

Cosecant function, secant function and cotangent function.

Cosecant function; cosecθ =hypotenuse/opposite =H/O.

Secant function; secθ =hypotenuse/adjacent =H/A.

Cotangent function; cotθ =adjacent/opposite =A/O.

Some examples depend on these formulas.

1)in a right angle triangle adjacent (x)=5c.m and hypotenuse (z)=13c.mthen find opposite with the help of Pythagoras theorem?

Solution-Pythagoras theorem is-

Z² =X² +Y²

Put the values in this formula-

(13)² = (5)² +Y²

169 = 25 + Y²

169 – 25 = Y²

144 = Y²

√144 = Y

Y = 12 c.m

Which is your answer.

2)In a right angle triangle x =6 meter and y = 8 meter then find z with the help of Pythagoras theorem?

Solution- z² =x²+ y²

Put the values-

Z² = (6)² + (8)²

Z² = 36 + 64

Z² =100

Z = √100

Z = 10 meter

Which is your answer.

3) In a right angle triangle adjacent =12, opposite =9 and hypotenuse =15, then find the sine, tangent and secant functions.

Solution –

a)      Sinθ =opposite/hypotenuse = O/H

Sinθ = 9/15 (put the values)

Sinθ = 0.6

Which is your answer.

b) Tanθ = O/A

Tanθ = 9/12 (put the values)

Tanθ = 0.75

Which is your answer.

c)       Sacθ = H/A

Secθ =15/12 (put the values)

Secθ = 1.25

Which is your answer.

These are basics knowledge about trigonometry. Trigonometry is full of formulas but if we don’t know about the basics formulas, then we cannot solve any question in trigonometry.