Trigonometry is a branch of mathematics.It shows relation of an angle with ratio of two side of a right triangle. Every right triangle has 6 trigonometric ratios.
1. Sine (sin)
2. Cosine (Cos)
3. Tangent (Tan)
4. Secant ( Sec)
5. Cosecant ( Cosec)
6. Cotangent ( Cot)
Each of the ratios has specific formula, which are given below:
Trigonometric formulas of 6 ratios:
Definition of trigonometric ratios
Ratio
is defined as a relation between two things. Trigonometric ratios represent
relation between two sides of a right triangle.
Definition of Sine: Sine is the ratio of the
opposite side of the angle and hypotenuse. Opposite side of the given angle divided
by hypotenuse of a right triangle is called sine.
Definition of Cosine: Adjacent side of the given
angle divided by hypotenuse of a right triangle is called Cosine,
Definition of Tangent: Opposite side of the given
angle divided by adjacent side of the given angle of a right triangle is called
Tangent.
Definition of Cotangent: Adjacent side of the given
angle divided by opposite side of the given angle of a right triangle is called
Cotangent.
Definition of Secant: Hypotenuse divided by
adjacent side of the given angle of the right triangle is called Secant.
Definition of Cosecant: Hypotenuse divided by
opposite side of the given angle of a right triangle is called Cosecant.
How to find the trigonometric ratios of a right triangle?
To find trigonometric ratios follow five steps below.
1. Select the ratio you want to find.
For example you want to find ratio of Sin.
2. Which angle to use.
It is very important to keep in mind which angle you are going to use. Because adjacent and opposite sides depend on it.
If given angle is Ө, use it in the ratio.Write it as Sin Ө.
3. Identify the sides ( Hypotenuse, Adjacent, and Opposite).
Find sides according to the given angle.
4. Substitute formula of the selected ratio.
Let's suppose opposite side of Ө is b and hypotenuse is c. So substitute the formula with the values in right triangle.
5. Solve the ratio.
Finally solve the ratio if it need further calculation.
In above example the ratio of Sin Ө will be:
Sin Ө = b / c
You must to know the formulas of trigonometric ratios to find the ratios.
1. Select the ratio you want to find.
For example you want to find ratio of Sin.
2. Which angle to use.
It is very important to keep in mind which angle you are going to use. Because adjacent and opposite sides depend on it.
If given angle is Ө, use it in the ratio.Write it as Sin Ө.
3. Identify the sides ( Hypotenuse, Adjacent, and Opposite).
Find sides according to the given angle.
4. Substitute formula of the selected ratio.
Let's suppose opposite side of Ө is b and hypotenuse is c. So substitute the formula with the values in right triangle.
5. Solve the ratio.
Finally solve the ratio if it need further calculation.
In above example the ratio of Sin Ө will be:
Sin Ө = b / c
You must to know the formulas of trigonometric ratios to find the ratios.
Let's find out the ratios of following triangle.
You have noticed that angle of the ratios is B which is represented by θ. So in that case opposite side of angle B is b and adjacent side of angle B is a.
In this triangle we have found ratios according to angle A.
What is hypotenuse?
Hypotenuse is opposite side of right angle.Here right angle is C,hence hypotenuse is c.
Let's solve another example.
In this triangle we have found ratios according to angle A.
Practice Problem:
Find out the following ratios according to angle B in the above right triangle.
1. Sin B
2.Cos B
3. Tan B
4. Cot B
5. Sec B
6. Cosec B
Answers