How can you learn the trigonometric formula?
Trigonometry is one of the most important branches of math and it deals basically with the sides and angles of the triangle. Hence it assists to find the missing angle or the sides of the triangle.Hence you can find the missing angles or the sides by the trigonometry formulas and ratios. In trigonometry either the angle can be measured in radian or in degrees.The trigonometric functions are even used in the integration and derivation.Once you are able to learn the trigonometric ratios,then it is easy to find the missing angles. You can learn the six important trigonometric ratios by the word SOHCAHTOA mnemonic.
What is Sohcahtoa mnemonic?
The term SOHCAHTOA can be defined by explaining the trigonometric ratios as the SOH stands for the Sin is equal to the Opposite over the Hypotenuse. The CAH stands for the Adjacent over the Hypotenuse. The TOA is equal to the Tan and is equal to the opposite over the adjacent. The three trigonometric ratios are given below
- SOH (Sin(θ))= Opposite/Hypotenuse
- CAH (Cos(θ)) = Adjacent/Hypotenuse
- TOA (Tan(θ))= Opposite/Adjacent
The remaining 3 trigonometric ratio are as follows
- Cosesθ= 1/(Sin(θ))= Hypotenuse/Opposite
- Sec θ =1/ (Cos(θ)) = Hypotenuse/Adjacent
- Cot θ =1/(Tan(θ))= Adjacent/Opposite
Six trigonometric ratios:
The six important trigonometric ratios are Sin, Cos, Tan, cosec, Sec and Cots, and you can’t solve any of the trigonometric questions without the trigonometric ratio.The six trigonometric ratios are given below:
| Functions | Abbreviation | Relationship to sides of a right triangle |
| Sine Function | sin | Opposite side/ Hypotenuse |
| Tangent Function | tan | Opposite side / Adjacent side |
| Cosine Function | cos | Adjacent side / Hypotenuse |
| Cosecant Function | cosec | Hypotenuse / Opposite side |
| Secant Function | sec | Hypotenuse / Adjacent side |
| Cotangent Function | cot | Adjacent side / Opposite side |
The trigonometric angles:
The trigonometric angles commonly used in trigonometry are 0°, 30°, 45°, 60° and 90°. You need to memorize the values of the Sin, Cos and Tan on these values, and it is not difficult to memorize the trigonometric angles values for all the trigonometric ratios. The values of the trigonometric angles are given below in the table
| Angles | 0° | 30° | 45° | 60° | 90° |
| Sin θ | 0 | ½ | 1/√2 | √3/2 | 1 |
| Cos θ | 1 | √3/2 | 1/√2 | ½ | 0 |
| Tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
| Cosec θ | ∞ | 2 | √2 | 2/√3 | 1 |
| Sec θ | 1 | 2/√3 | √2 | 2 | ∞ |
| Cot θ | ∞ | √3 | 1 | 1/√3 | 0 |
The same way, we can use the trigonometric angles beyond 90 degrees.
Sides of the right angle triangle:
The three sides of the right angle triangle are Opposite side, Adjacent side and the Hypotenuse. We are discussing the three sides of the triangle below:
Adjacent side:
The adjacent side is the side of the right angle triangle which is along or adjacent to the angle of the triangle. The adjacent side has the angle and is also called the base of the right angle triangle.
Opposite side:
The opposite side is the side which is opposite to the angle of the triangle and it is also known to be as the perpendicular of the triangle. The perpendicular is at the right angle of the triangle.This is the main reason triangle is called right angle triangle.
Hypotenuse:
The hypotenuse is the largest side of the triangle and it is making an angle with the base of the triangle.
Conclusion:
The triangles are the most important shape in trigonometry and we are using the right angle triangle to find various measurements. The trigonometric ratios are the key for finding a missing side.
