# Why use the Sohcahtoa Mnemonic?

SOHCAHTOA” is a helpful mnemonic for remembering the definitions of trigonometric functions.

Trigonometry is one of the most difficult subjects in mathematics. Main reason is the ratio and geometric angles.You need to remember and understand various ratios to solve questions. You need to understand what the right angle triangle is and its ratios. The different sides of the triangles like the Adjacent side, Opposite side and Hypotenuse.

Various sides are equated to identify angles and ratios like the Sin, Cos, Tan. You may find the Sin, Cos, Tan ratio, the Sohcahtoa ↱ is a mnemonic which makes it easy to remember the ratios. Sohcahtoa calculator is especially designed to solve the Sin, Cos, Tan ratio. You can learn mnemonic meaning to learn the ratio of the right angle triangles.

**What is Sohcahtoa?**

The right angle triangle is used to solve the various trigonometric problems. SOH CAH TOA is a combination of three word “SOH”, Sin is equal to Opposite Side over Hypotenuse. “CAH”, Cos is equal to Adjacent Side over Hypotenuse, “TOA”, Tan is equal to Adjacent Side over Opposite Side. Trig calculator is a simple way to identify the various ratios and its resultant sides. You can identify the various sides and their impact in applying the pythagorean theorem and area of the triangle.

**SOH = Sin**** = Opposite Side / Hypotenuse**

**CAH = Cos**** = Adjacent Side / Hypotenuse**

**TOA = Tan**** = Opposite Side / Adjacent Side**

The Sohcahtoa calculator is a simple way to identify the various sides and their correlation with each other. You may find it difficult to understand the various ratios and their ultimate relation.

**How does the Sohcahtoa apply?**

Consider a right angle triangle and its angle is 20 degrees, the Opposite side is 10 cm and find the hypotenuse.

Given:

Angle = 20° degree

Opposite side = 10 cm

Hypotenuse = ?

Solution:

Here first you need to identify the what is the relationship between the two side:

Sin = Opposite Side / Hypotenuse

If you are using the trigonometry calculator,then it is the Sin = Opposite Side / Hypotenuse. It is easy to identify the various terms like the angles, to find the radius of the right angle triangle.

sin(20°) = 10/r

The sin(20°) is the 0.3420, the opposite side is the “r” is the hypotenuse

r{sin(20°)} = 10

r = 10/sin(20°)

r = 10/0.3420

Now by rearranging all the terms, you can identify r = 29.239 cm. It is the hypotenuse of the right angle triangle.

r = 29.239 cm

The Hypotenuse r = 29.239, in this case, this is the main reason. We can identify the various sides in a matter of seconds.When using the Sohcahtoa calculator, you can identify the various terms and their effect on the right angle triangle.

**The Reverse Trigonometric ratios: **

When you are able to remember the mnemonic, then it is possible to remember the reverse angle.You may be amazed to learn that it is possible to remember the Cosec,Sec, Cot . This is the reverse of the forward ratios like the Sin = Opposite Side / Hypotenuse. The Cos = Adjacent Side / Hypotenuse, and Tan = Opposite Side / Adjacent Side

**Cosec**** = ****Sin ****-1**** = Hypotenuse / Opposite Side **

**Sec**** ****= ****Cos ****-1****= Hypotenuse / Adjacent Side **

**Cot ****= ****Tan ****-1**** =Adjacent Side / Opposite Side **

The reverse trigonometric ratios like the Cosec, Sec,Cot are as important to learn as the forward trigonometric ratios. If you are able to learn the forward ratios by the simple Mnemonic. Then it is possible to remember the reverse ratios as these are perfectly reverse to forward ratios.

The Sohcahtoa calculator is assisting to find the forward trigonometric ratio and reverse trigonometric ratios. You can apply the various trigonometric ratios of the right angle triangle. It is one of the simple way to identify the various sides and their application is

**Conclusion:**

The trigonometric applications are applied even in integration and derivation. If the students are able to learn the trigonometric ratios only by learning the word “soh cah toa”. Then it is great as the simple word is the solution to the whole problem. You can learn all the trigonometric ratios by using the Sohcahtoa calculator, it is a simple solution for the students. The new techniques are used to teach the students and the “sohcahtoa” is one of the good examples of this creative way to teach trigonometry ratio.

##### Mathew L

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