How To Use Sohcahtoa?

How To Use Sohcahtoa?

Sohcahtoa: SOHCAHTOA is a mnemonic device that is used in mathematics to remember the definitions of the three most common trigonometric functions. This lesson will explain each one and give examples, and you’ll have the opportunity to take a quiz at the end to solidify what you’ve learned.

Sine, cosine, and tangent are the three main functions in trigonometry. They’re all based on ratios obtained from a right triangle. Before we can discuss what ratios work for which function, we need to label a right triangle.

How To Use Sohcahtoa?

The ratios that allow you to determine the sine, cosine, and tangent of a right triangle are:Opposite is the side opposite the angle in question, adjacent is the side next to the angle in question, and the hypotenuse is the longest side of a right triangle. The hypotenuse is always opposite the right angle.

  • The sine of an angle is equal to the side opposite the angle divided by the hypotenuse.
  • The cosine of an angle is equal to the side adjacent to the angle divided by the hypotenuse.
  • The tangent of an angle is equal to the side opposite the angle divided by the side adjacent to the angle.

    SOHCAHTOA. A way of remembering how to compute the sine, cosine, and tangent of an angle. SOH stands for Sine equals Opposite over Hypotenuse. CAH stands for Cosine equals Adjacent over Hypotenuse. TOA stands for Tangent equals Opposite over Adjacent.

    SOH = Sine is Opposite over Hypotenuse. CAH = Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent.

    SineCosine and Tangent are the main functions used in Trigonometry and are based on a Right-Angled Triangle. Before getting stuck into the functions, it helps to give a name to each side of a right triangle: … “Adjacent” is adjacent (next to) to the angle θ “Hypotenuse” is the long one.

Sohcahtoa Calculator

Sohca…what? Just an easy way to remember how Sine, Cosine and Tangent work:

Soh…
Sine = Opposite / Hypotenuse
…cah…
Cosine = Adjacent / Hypotenuse
…toa
Tangent = Opposite / Adjacent

Right Triangle

OK, let’s see what this is all about.

Firstly, the names Opposite, Adjacent and Hypotenuse come from the right triangle:

triangle showing Opposite, Adjacent and Hypotenuse

 

  • “Opposite” is opposite to the angle θ
  • “Adjacent” is adjacent (next to) to the angle θ
  • “Hypotenuse” is the long one

examples of Opposite, Adjacent and Hypotenuse

Adjacent is always next to the angle

And Opposite is opposite the angle

Sine, Cosine and Tangent

And SineCosine and Tangent are the three main functions in trigonometry.

They are often shortened to sincos 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.

For a triangle with an angle θ , the functions are calculated this way:

Sine:
soh…
sin(θ) = opposite / hypotenuse
Cosine:
…cah…
cos(θ) = adjacent / hypotenuse
Tangent:
…toa
tan(θ) = opposite / adjacent

 

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

A 30° triangle has a hypotenuse (the long side) of length 2, an opposite side of length 1 and an adjacent side of √3, like this:

30° triangle

Now we know the lengths, we can calculate the functions:

Sine
soh…
sin(30°) = 12 = 0.5
Cosine
…cah…
cos(30°) = 1.732…2 = 0.866…
Tangent
…toa
tan(30°) = 11.732… = 0.577…

(get your calculator out and check them!)

Sohcahtoa Worksheet

A way to remember the definitions of the three most common trigonometry functions: sin, cos and tan.

Used as a memory aid for the definitions of the three common trigonometry functions sine, cosine and tangent. When spoken it is usually pronounced a bit like “soaka towa”.

SOH Sine = Opposite over Hypotenuse.
 sin
x
=
O
H
CAH Cosine = Adjacent over Hypotenuse.
 cos
x
=
A
H
TOA Tangent = Opposite over Adjacent.
 tan
x
=
O
A

How To Use Sohcahtoa

These ratios can be difficult to remember. You might easily get confused and not remember which side goes where. SOHCAHTOA is a mnemonic device helpful for remembering what ratio goes with which function.

  • SOH = Sine is Opposite over Hypotenuse
  • CAH = Cosine is Adjacent over Hypotenuse
  • TOA = Tangent is Opposite over Adjacent

With these properties, you can solve almost any problem related to finding either a side length or angle measure of a right triangle. SohCahToa can ensure that you won’t get them wrong.

What Is Sohcahtoa

A way of remembering how to compute the sine, cosine, and tangent of an angle.

SOH stands for Sine equals Opposite over Hypotenuse.

CAH stands for Cosine equals Adjacent over Hypotenuse.

TOA stands for Tangent equals Opposite over Adjacent.


Sohcahtoa Examples

Example:

Find the values of sin θ, cos θ, and tan θ in the right triangle shown.

Answer:

sin θ = 3/5 = 0.6

cosθ = 4/5 = 0.8

tanθ = 3/4 = 0.75

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