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 sin**θ** of opposing angle

we know that sin\theta \quad =\frac { Perpendicular }{ Hypotenuse }

sin**θ** = 2/4

sin**θ**= 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 cos**θ** of angle C

**Given**

Base = 2 cm

Hypotenuse = 4 cm **To Find**

cos**θ**

**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 tan**θ** of angle C

**Given**

Base = 4 cm

Height = 4 cm

**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 tan**θ**

The opposing degree of tan**θ** 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.