Question

What is the formula of SOH CAH TOA?

Answer 1

Hint: We will draw a right angle triangle and then we need to name the sides according to the given angle i.e opposite, adjacent and hypotenuse. We know that sin, cos and tan are the three main functions in trigonometry. To calculate this, we need to divide one side with another side. Thus, to remember this, we will use the word ‘sohcahtoa’ word. Thus, we will get the formula of all three using this and thus will get the final output.

Complete step-by-step answer:
First, we will draw a right angle triangle:
Fig

Here, from the figure, we can say that,
Let angle A be \[\theta \] .
Opposite – Means opposite to given angle (BC).
Adjacent – Means next to the given angle (AC).
Hypotenuse – Means the longest side of the right angle triangle (AB).
We know that,
Sine, Cosine and Tangent are the three main functions in trigonometry.
They are often shortened to sin, cos and tan.
The calculation is simply one side of a right angled triangle divided by another side ... we just have to know which sides, and that is where "sohcahtoa" helps.
The best mnemonics for remembering formulas of sine, cosine and tangent in trigonometry are SOH, CAH and TOA respectively. These formulas can be written as given below:
Suppose H is the hypotenuse, O is the opposite side and A is the adjacent side of a right triangle.
For a triangle with an angle \[\theta \] the functions are calculated this way:
SOH: \[Sin\theta = \dfrac{{Opposite}}{{Hypotenuse}}\]
CAH: \[\operatorname{Cos} \theta = \dfrac{{Adjacent}}{{Hypotenuse}}\]
TOA: \[\operatorname{Tan} \theta = \dfrac{{Opposite}}{{Adjacent}}\]

Note: Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. Well there is an easy way to find ‘sohcahtoa’ and easy to remember:
1) Sailors Often Have Curly Auburn Hair Till Old Age.
2) Some Old Horses Can Always Hear Their Owners Approach.
3) Some Old Hen Caught Another Hen Taking One Away.