# SOHCAHTOA - Formulas & How to Solve?

## Trigonometery SOHCAHTOA

Trigonometry has been a tricky but easy subject in mathematics. Those who know how to simplify fractions can deal with trig identities and ratios easily.

One of the major trigonometric functions is SOHCAHTOA, which is the topic unveiled in the article below.

## Definition:

In trigonometry, SOHCAHTOA is a mnemonic that defines triangle ratios, such that:

• SOH = sine
• COH = cosine
• TOA = tangent

## SOHCAHTOA Formulas:

• Sine = Opposite / Hypotenuse
• Cosine = Adjacent / Hypotenuse
• Tangent = Opposite / Adjacent

## How to Remember SOHCAHTOA Mnemonics?

For some students, SOHCAHTOA ratios can be tricky to remember. So in this situation, the following sentences will them understand the mnemonics better:

• Some Old Hag Cracked All Her Teeth On Asparagus
• Silly Old Harry Caught A Huge Trout Out Angling
• Sucking On Hard Candy Always Has Totally Overwhelming Awesomeness
• Somebody Obviously Hates Creativity And Has Tiny Opera Actors
• Some Old Hippy Caught Another Hippy Tripping On Acid

## Tips to Remember Sin Cos Tan Table:

• First, you need to remember that the angles are in the order
• You can remember the first row of sin as
• The same is the case with cosine value but in the reverse order
• When it comes to tangent, its value can be determined by dividing equivalent values of sine and cosine

The SOHCAHTOA calculator also functions by considering the same chart values as trig standards.

## Application of Sin Cos Tan In Real Life:

In daily life, we all use different applications of SOHCAHTOA trigonometry. Let us discuss one such application in the following example:

### Question Statement:

A ladder leans against a brick wall making an angle of 30 degrees with the horizontal. If the base of the ladder is at a distance of 10 ft from the wall, then how high up the wall does the ladder reach?

### Solution:

#### Data Given:

• Adjacent side = 10 ft
• Opposite side = x ft = ?

#### Calculations:

tan 35 = x / 10

x = 10 tan 35

x = 10 * 0.700

x = 7 ft

This is the required answer and can be verified with the SOHCAHTOA calculator by inputting the side and angle values given.

## SOHCAHTOA Table:

Radians 0 π/6 π/4 π/3 π/2
sin 0 1/2 1/√2 √3/2 1
cos 1 √3/2 1/√2 1/2 0
tan 0 1/√3 1 √3 Not Defined

## Sin Cos Tan on Unit Circle:

By using a unit circle, you can determine the values of sine, cosine, and tangent very easily.

A unit circle has a radius of 1 and is centered about the origin of the coordinate system (0, 0). By considering these, the trig ratios are given as follows:

### Who Is the Father of Trigonometry?

Hipparchus was the Greek Mathematician who is considered the father of Trigonometry. He developed the technique in the second century BC (Before Christ).

### What Branch of Math Is SOHCAHTOA?

The mnemonic SOHCAHTOA belongs to Trigonometry, a well-known branch of applied mathematics.

### What are Basic Trigonometric Identities?

The following are the basic trig identities that you should remember by heart:

• Reciprocal Identities
• Pythagorean Identities
• Even and Odd Angle Formula
• Cofunction identities (in Degrees)
• Sum and Difference Identities
• Double Angle Identities
• Inverse Trigonometry Formulas
• Triple Angle Identities
• Half Angle Identities
• Sum to Product Identities
• Product Identities

## Summary:

Illustratively, SOHCAHTOA formulas outline sine, cosine, and tangent as ratios within a right triangle. To ease memorization, mnemonics like "Some Old Hag Cracked All Her Teeth On Asparagus" or "Silly Old Harry Caught A Huge Trout Out Angling" prove invaluable. Understanding the mnemonic aids in recalling trigonometric ratios effortlessly.

Furthermore, remembering the sin, cos, tan table sequence facilitates quick calculations. In practical scenarios, such as determining the height of a ladder against a wall, applying these trigonometric functions becomes indispensable. Through basic calculations like tan(35°) = x/10, trigonometry seamlessly solves real-life problems.