Sohcahtoa: The Simple Way to Calculate Sine, Cosine, and Tangent

Sohcahtoa - Photo by Kyle Sherrets from Flickr
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Aug 14, 2020 02:00 PM

A branch of mathematics, Trigonometry is often defined as one of the hardest parts to study. Whereas, trigonometry has numerous applications for everyday life problems like calculating height, measure distance between objects, and satellite navigation system. It is also useful for geography, as well as the astronomy field.

Trigonometry is mostly dealing with triangles and angles, particularly the relationship and ratios between angles and sides in triangles. These aspects somehow make people confuse to calculate manually. Therefore, the demand for trigonometry calculator becomes high. 

Sohcahtoa, a trigonometry calculator will help you to solve two popular cases when trigonometry is needed. You may use it to find the values of sine, cosine, and tangent as well as search the missing angle in a right triangle. Keep reading to know more about trigonometry, sohcahtoa calculator, and how to use it.

Understanding Trigonometry

Sohcahtoa - Photo by vibho from Flickr

The word trigonometry rooted in Greek trigonon which has meaning "triangle" and metron "measure". This branch of mathematics is always related to angles and triangles in its use. In general, trigonometry has many applications. The sine and cosine are fundamental to define periodic phenomena.

Trigonometry has also been used in different fields of science and engineering. Those include music, acoustics, electronics, medicine, biology, chemistry, meteorology, mechanical, civil engineering, and even economics. It is also used in astronomy and geography.

1. Trigonometry Calculator to Find Sin, Cos, Tan, Cot, Sec, Csc

Enter the chosen angle in degrees or radians to find trigonometric functions of an angle. You can find six most popular trigonometry functions underneath the calculator.

The three basic ones namely sine, cosine, and tangent, and other reciprocals such as cosecant, secant, and cotangent. Besides, the right triangle will be shown if the angle is acute. It helps you to understand how the functions will be interpreted.

2. Trigonometry Calculator to Solve The Right Triangle

You can find missing sides or angles of the right triangle. You only need two given values in the case of two sides, area and one side, one side and one and angle.

Sohcahtoa Definition

Sohcahtoa is the way to remember the definitions of trigonometry functions: sin, cos, and tan. In other words, Sohcahtoa is also defined as a helpful mnemonic to ease you remember the three basic trigonometry ratios used for missing angles and sides in a right triangle.

Here is the way of remembering trigonometry functions:

  • Opposite leg: opposite one of the acute angles
  • Adjacent leg: is in the next of acute angle
  • Hypotenuse leg: is in the right angle, the long one

Sine, cosine, and tangent are the three main functions in trigonometry. They are commonly called sin, cos, and tan. The calculation is only one side of a right-angled triangle divided by another side. In this case, you just need to understand which side and let sohcahtoa helps you.

  • SOH means Sine= Opposite over Hypotenuse / sin x = O/H
  • CAH means Cosine= Adjancent over Hypotenuse/ Cos x=A/H
  • TOA means Tangent= Opposite over Adjacent/ tan x=O/A

Example: Decide the sine, cosine, and tangent of 30°?

On the long side, the hypotenuse of 30° has length 2, the opposite side of length 1, and an adjacent side of √3.

Here the way you calculate the functions:

sin(30°) = Opposite/Hypotenuse

     = 1/2  

     = 0.5

cos(30°) = Adjancent/Hypotenuse

              = √3/2 

      = 1.732/2  

      = 0.866

tan(30°) = Opposite/Adjacent

      = 1/ √3

      = 1/11.732  

      =  0.577

Tips to remember Sohcahtoa

  • Sailors Often Have Curly Auburn Hair Till Old Age (SOHCAHTOA).
  • Some Old Horses Can Always Hear Their Owners Approach (SOHCAHTOA).
  • Some Old Hen Caught Another Hen Taking One Away (SOHCAHTOA).

Sohcahtoa for Right Triangle

Adjacent is located always next to the angle. While the opposite is the opposite of the angle.

Here is the way of remembering trigonometry functions:

  • Opposite leg: opposite one of the acute angles
  • Adjacent leg: is in the next of acute angle
  • Hypotenuse leg: is in the right angle, the long one

Remember, sohcahtoa is only used for the right triangles. If you wish to work with the oblique triangle, you may learn about Math analysis and Trigonometries such as sines and cosines. Use sohcahtoa where there are two of the side lengths given and you need to find the third side.

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