Trigonometry is one of the most important branches of math and it deals basically with the sides and angles of the triangle. You’ll get here the Trigonometric Formula and SOHCAHTOA Mnemonic.
Hence it assists in finding the missing angle or the sides of the triangle. Hence you can find the missing angles by the trigonometry formulas. In trigonometry either the angle can be measured in radians or degrees.
The trigonometric functions are even used in the integration and derivation. Once you can learn the trigonometric ratios, it is easy to find the missing angles. You can learn the six important trigonometric ratios by the word SOHCAHTOA mnemonic. The SOHCAHTOA calculator by calculator-online.net is a simple way to learn all the trigonometric ratios.
What is the 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 ratios are as follows
- Cosesθ= 1/(Sin(θ))= Hypotenuse/Opposite
- Sec θ =1/ (Cos(θ)) = Hypotenuse/Adjacent
- Cot θ =1/(Tan(θ))= Adjacent/Opposite
The SOHCAHTOA calculator is a method to learn and remember trigonometric ratios.
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 |
| e 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 |
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The Trigonometric Formula
The trigonometric formulas are mathematical tools that relate the angles and sides of triangles, helping us understand and solve various geometric and real-world problems.
Trigonometric angles
The trigonometric angles 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 angle values for all the trigonometric ratios.
The values of the trigonometric angles are given below in the table. The SOHCAHTOA calculator is a method to learn and remember trigonometric ratios.
| 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 |
In the same way, we can use trigonometric angles beyond 90 degrees.
Sides of the right angle triangle
The three sides of the right-angle triangle are the Opposite side, the adjacent side, and the Hypotenuse. We are deliberating the three sides of the triangle here:
1. 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 called the base of the right-angle triangle. The SOHCAHTOA calculator is a way to learn and remember trigonometric ratios.
2. Opposite side
The opposite side is the side that is opposite to the angle of the triangle and it is also known to be the perpendicular of the triangle. The perpendicular is at the right angle of the triangle. This is the main reason a triangle is called a right-angle triangle.
3. Hypotenuse
The hypotenuse is the largest side of the triangle and it is making an angle with the base of the triangle.
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How do you remember the trigonometry formula trick?
One of the most widely used acronyms for recalling trigonometric ratios is SOHCAHTOA, representing “Sine Opposite Hypotenuse, Cosine Adjacent Hypotenuse, Tangent Opposite Adjacent.” To aid in remembering this acronym, create a mnemonic phrase using these letters such as “She Offered Her Child A Heaping Teaspoon Of Applesauce.”
What is the acronym for trigonometric functions?
There isn’t a widely recognized single acronym for all trigonometric functions, but there’s a handy mnemonic that uses the first letters of the most common ones: SOH CAH TOA.
Each letter stands for a function and its corresponding side in a right triangle:
- Sine = Opposite / Hypotenuse
- Cosine = Adjacent / Hypotenuse
- Tangent = Opposite / Adjacent
Remember SOH CAH TOA, and trigonometry won’t be such a pain in the… hypotenuse.
Last Word
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 to finding a missing side.