What are Six Trigonometry Functions?
The six trigonometric functions have formulae for the right-angled triangles, the formulae help in identifying the lengths of the sides of a right-angled triangle, lets take a look at all those formulae,
| Trigonometric Functions | Formulae |
|---|---|
| sin θ | |
| cos θ | |
| tan θ | |
| cosec θ | |
| sec θ | |
| cot θ |
The below table shows the values of these functions at some standard angles,
| Function | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| [Tex]sin\theta = \frac{P}{H}[/Tex] | [Tex]0[/Tex] | [Tex]\frac{1}{2}[/Tex] | [Tex]\frac{1}{\sqrt2}[/Tex] | [Tex]\frac{\sqrt3}{2}[/Tex] | [Tex]1[/Tex] |
| [Tex]cos\theta = \frac{B}{H}[/Tex] | [Tex]1[/Tex] | [Tex]\frac{\sqrt3}{2}[/Tex] | [Tex]\frac{1}{\sqrt2}[/Tex] | [Tex]\frac{1}{2}[/Tex] | [Tex]0[/Tex] |
| [Tex]tan\theta = \frac{sin\theta}{cos\theta}=\frac{P}{B}[/Tex] | [Tex]0[/Tex] | [Tex]\frac{1}{\sqrt3}[/Tex] | [Tex]1[/Tex] | [Tex]\sqrt3[/Tex] | ∞ |
| [Tex]cosec\theta = \frac{H}{P}[/Tex] | ∞ | [Tex]2[/Tex] | [Tex]\sqrt2[/Tex] | [Tex]\frac{2}{\sqrt3}[/Tex] | [Tex]1[/Tex] |
| [Tex]sec\theta = \frac{H}{B}[/Tex] | [Tex]1[/Tex] | [Tex]\frac{2}{\sqrt3}[/Tex] | [Tex]\sqrt2[/Tex] | [Tex]2[/Tex] | ∞ |
| [Tex]cot\theta = \frac{B}{P}[/Tex] | ∞ | [Tex]\sqrt3[/Tex] | [Tex]1[/Tex] | [Tex]\frac{1}{\sqrt3}[/Tex] | [Tex]0[/Tex] |
Note: It is advised to remember the first 3 trigonometric functions and their values at these standard angles for ease of calculations.
Six Trigonometric Functions
Trigonometry can be defined as the branch of mathematics that determines and studies the relationships between the sides of a triangle and the angles subtended by them. Trigonometry is used in the case of right-angled triangles. Trigonometric functions define the relationships between the 3 sides and the angles of a triangle. There are 6 trigonometric functions mainly.
Before going into the study of the trigonometric functions we will learn about the 3 sides of a right-angled triangle.
The three sides of a right-angled triangle are as follows,
Right Triangle
- Base: The side(RQ) on which the angle θ lies is known as the base.
- Perpendicular: It is the side(PQ) opposite to the angle θ in consideration.
- Hypotenuse: It is the longest side(PR) in a right-angled triangle and opposite to the 90° angle.
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