Basic Trigonometry Function

In this post we will discuss the basic trigonometry function which is important for the point of view of Grade 11. You have previously studied the concepts in your earlier classes but i want to revisit the chapter for the benefits of the students.

Here we will study the important trigonometry functions, their expressions and their values. All the functions will be explained with the help of diagram and after that we will also solve some problems for better conceptual understanding.

Trigonometry Function

The best way to understand trigonometry function is by taking help of a right angled triangle.
Let ABC is the right angles triangle with angle B as 90 degree

From the above illustration you can observe that:
AB = height of triangle
BC = Base of triangle
AC = hypotenuse of triangle
θ is the angle C under consideration

Now taking help of the above triangle we will define following trigonometry function:
sinθ, cosθ, tanθ, cosecθ, secθ, cotθ

Sin Function (sinθ)

sin\theta \quad =\frac { side\quad opposite\quad to\quad angle\theta }{ Hypotenuse } \\\ \\ sin\theta \quad =\frac { Perpendicular }{ Hypotenuse }

Example
In right triangle ABC, height is 2 cm and hypotenuse is 4 cm. Then find the sinθ of opposing angle

we know that sin\theta \quad =\frac { Perpendicular }{ Hypotenuse }
sinθ = 2/4
sinθ= 1/2
Hence value of sinθ of opposing angle is 1/2

Cosine Function (cosθ)

cos\theta \quad =\frac { Base }{ Hypotenuse }

Example
In right triangle ABC, base is 2 cm and hypotenuse is 4 cm. Then find the cosθ of angle C

Given
Base = 2 cm
Hypotenuse = 4 cm

To Find
cosθ

cos\theta \quad =\frac { Base }{ Hypotenuse } \\\ \\ cos\theta \quad =\quad \frac { 2 }{ 4 } \\\ \\ cos\theta \quad =\frac { 1 }{ 2 }

Tan Function (tanθ)

tan\theta \quad =\frac { opposite\quad side\quad to\quad angle\theta \quad }{ adajcent\quad side\quad to\quad angle\quad \theta } \\\ \\ tan\theta \quad =\frac { Perpendicular }{ Base } \

Example
In right triangle ABC, base is 4 cm and height is 4 cm. Then find the tanθ of angle C

Given
Base = 4 cm
Height = 4 cm

tan\theta \quad =\frac { Perpendicular }{ Base } \\\ \\ tan\theta \quad =\frac { 4 }{ 4 } \quad =\quad 1\

Cosecθ, Secθ & Cotθ

These angle can be easily defined as

cosec\theta =\quad \frac { 1 }{ sin\theta } \quad =\frac { Hypotenuse }{ Perpendicular } \\\ \\ \ sec\theta =\quad \frac { 1 }{ cos\theta } \quad =\frac { Hypotenuse }{ Base } \\\ \\ \ cot\theta =\quad \frac { 1 }{ tan\theta } \quad =\frac { Base }{ Perpendicular } \ \ \ \

Important Trigonometry Values

My request to all the students is to remember all the values as the above data is needed to solve questions. Some important points that will help you remember above data is as follows:

a. The values of sinθ and cosθ run opposite to each other

For Example:
sin 0° = 0
Opposite of 0° is 90°
cos 90°=0
Hence the value of sin and cos in opposing degree is same

b. Remembering values of tanθ

The opposing degree of tanθ are reciprocal of each other
i.e values of tanθ and tan(90- θ) are reciprocal

c. The values of cosecθ and secθ run opposite to each other

Values of cosecθ and sec(90- θ) are equal

This technique is similar to what we have seen in sin & cos relationship

I hope that you have now understood that basic concepts of trigonometry functions.
If you want to solve questions of Class 11, you need to remember all the data that has been mentioned above.

Please don’t get intimidated by the formulas and numbers used in trigonometry, its just a matter of time to get used to the concept and then its all simple and easy.