BASICS OF TRIGONOMETRY

INTRODUCTION TO TRIGONOMETRY

The word TRIGONOMETRY is comprised of 2 words. TRIGONO & METRON. TRIGONO means Triangle & METRON means measure.

TRIGONO + METRON = TRIGONOMETRY

It is a misconception that Trigonometry is only about study of Right angle triangle, it about all the triangles. But it is mainly used in Right angle triangle.

TRIGONOMETRY ANGLES OF RIGHT ANGLE TRIANGLE

Being right angle triangle, one angle is 90^o. Assume 2^nd angle as

\theta

. Lets call this angle q as trigonometric angle. [Why??? We will see later on]

So, the 3^rd angle is (180^o – 90^o – $\theta$ ) = 90^o – $\theta$ [Sum of 3 sides of a triangle is 180^o]

Everything here will be related to this Trigonometric angle $\theta$ . Lets more understand this, after doing Trigonometric sides.

TRIGONOMETRY SIDES OF RIGHT ANGLE TRIANGLE

In trigonometry, 3 sides of a right angle triangle are given special names, which are called Trigonometric sides. The name given to the 3 Trigonometric sides are PERPENDICULAR, BASE & HYPOTENUSE. Lets discuss it one by one.

PERPENDICULAR

The side opposite to Trigonometric angle $\theta$ is known as Perpendicular.

In our Triangle ABC, the side opposite to angle $\theta$ is AC. So the side AC is Perpendicular.

BASE

Base is the side which is adjacent to angle $\theta$ . OR the side between 90^o & Angle $\theta$ .

In our Triangle ABC, side between 90^o & Angle $\theta$ is AB. So, the side AB is Base.

HYPOTENUSE

The side opposite to 90^o angle is known as Hypotenuse. Hypotenuse is the largest of the 3 sides.

In our Triangle ABC, the side opposite to angle 90^o is BC. So, the side BC is Hypotenuse.

NOTE:

All these sides are w.r.t angle $\theta$ , which we have called as Trigonometric angle. Means,

AB is Perpendicular w.r.t angle $\theta$ .

BC is Base w.r.t angle $\theta$ .

AC is Hypotenuse w.r.t angle $\theta$ .

What will happen, if we change the Trigonometric angle??? Lets see……

Changes in Trigonometry Sides on Changing Trigonometry Angle

In this case, let’s assume angle 90 $– \theta$ as Trigonometric angle.

We already know,
Perpendicular: Side opposite to Trigonometric angle $\theta$ .
Base: Side adjacent to Trigonometric angle $\theta$ . OR Side between 90^o & Trigonometric angle $\theta$ .
Hypotenuse: Side opposite to 90^o angle.

In previous case, $\theta$ was Trigonometric angle. And in this case, 90 $– \theta$ is the Trigonometric angle.

So, the 3 Trigonometric sides w.r.t new Trigonometric angle 90 $-\theta$ are

AB is Perpendicular w.r.t angle $\theta$ .
Why??? Because perpendicular is the side, which is opposite to Trigonometric angle. Here Trigonometric angle is 90 $-\theta$ . And side opposite to 90 $-\theta$ angle is AB.

AC is Base w.r.t angle $\theta$ . Why??? Think on your side and comment below.

BC is Hypotenuse w.r.t angle $\theta$

Refer the below animation for more clarity.

Have you noticed that Hypotenuse does not change. It remain fixed. Think over it.
Hypotenuse is the side opposite to 90^oangle. For a triangle, 90^oangle is fixed, so Hypotenuse is also fixed. Moreover, Hypotenuse is the largest of the 3 sides. Largest sides, will remain the largest side.

Got the point. In case of any doubt. Small to Big, just comment below. In case you want to ask something apart from this topic, launch your doubt in Trigonometric forum.

Do not forget to solve the question given below.

Best of LUCK.

Watch the Complete Video of this Lecture with help of Animation Tool.

(Visualize the concept, in totally different way)

Questions:

Q1) Identify the 3 Trigonometric sides in figure given below.

Q2) Identify the 3 Trigonometric sides in figure given below.

Q3) Match the following:

A. PERPENDICULAR

B. BASE

C. HYPOTENUSE

i. Side Opposite to 90 Degree Angle.

ii. Side opposite to Trigonometric Angle.

iii. Side between Trigonometric angle & 90 degree angle.

Enter your answers below in the comments.