Sohcahtoa Calculator

The SOHCAHTOA calculator follows this particular mnemonics to resolve for trigonometric functions of a right-angled triangle.

What Exactly SOHCAHTOA Is?

In Trigonometry, SOHCAHTOA is defined as follows:

SOH (Sin(θ))= Perpendicular/Hypotenuse

CAH (Cos(θ)) = Base/Hypotenuse

TOA (Tan(θ))= Perpendicular/Base

Our SOHCAHTOA solver also considers the same correlated formulas so as to depict triangle sides and angles measurements.

How SOHCAHTOA Helps In Remembering Trig Ratios?

Most of us still find it tricky and confusing to remember trigonometry ratios. No doubt only three sides and angles are there to deal with. But the probability of exact recalling every time is still faded for us.

Putting things simple now, let’s have a look at the following triangle below:

In this triangle, three sides are labelled as:

Opposite (Perpendicular)

The side that is opposite to acute angle

Adjacent (Base)

The side that is connected to acute angle and opposite

Hypotenuse

The longest side of Right Angle triangle whose one end is connected to base, while other is connected to opposite

SOHCAHTOA Measures of Popular Angles:

Trigonometry runs around some basic angle measurements that form the basis of angle and side calculations under the subject. These are given as follows:

	$$ {\displaystyle \sin \theta } $$	$$ {\displaystyle \cos \theta } $$	$$ {\displaystyle \tan \theta =\sin \theta {\Big /}\cos \theta } $$
0° = 0 radians	$$ {\displaystyle {\frac {\sqrt {\mathbf {\color {blue}{0}} }}{2}}=\;\;0} $$	$$ {\displaystyle {\frac {\sqrt {\mathbf {\color {red}{4}} }}{2}}=\;\;1} $$	$$ {\displaystyle \;\;0\;\;{\Big /}\;\;1\;\;=\;\;0} $$
30° = π/6 radians	$$ {\displaystyle {\frac {\sqrt {\mathbf {\color {teal}{1}} }}{2}}=\;\,{\frac {1}{2}}} $$	$$ {\displaystyle {\frac {\sqrt {\mathbf {\color {orange}{3}} }}{2}}} $$	$$ {\displaystyle \;\,{\frac {1}{2}}\;{\Big /}{\frac {\sqrt {3}}{2}}={\frac {1}{\sqrt {3}}}} $$
45° = π/4 radians	$$ {\displaystyle {\frac {\sqrt {\mathbf {\color {green}{2}} }}{2}}={\frac {1}{\sqrt {2}}}} $$	$$ {\displaystyle {\frac {\sqrt {\mathbf {\color {green}{2}} }}{2}}={\frac {1}{\sqrt {2}}}} $$	$$ {\displaystyle {\frac {1}{\sqrt {2}}}{\Big /}{\frac {1}{\sqrt {2}}}=\;\;1} $$
60° = π/3 radians	$${\displaystyle {\frac {\sqrt {\mathbf {\color {orange}{3}} }}{2}}} $$	$$ {\displaystyle {\frac {\sqrt {\mathbf {\color {teal}{1}} }}{2}}=\;{\frac {1}{2}}} $$	$$ {\displaystyle {\frac {\sqrt {3}}{2}}{\Big /}\;{\frac {1}{2}}\;\,={\sqrt {3}}} $$
90° = π/2 radians	$$ {\displaystyle {\frac {\sqrt {\mathbf {\color {red}{4}} }}{2}}=\;\,1} $$	$$ {\displaystyle {\frac {\sqrt {\mathbf {\color {blue}{0}} }}{2}}=\;\,0} $$	$$ {\displaystyle \;\;1\;\;{\Big /}\;\;0\;\;=} Undefined $$

Basic SOHCAHTOA Ratios:

Following are the most broadly implemented SOHCAHTOA ratios in calculus and analytic geometry:

Sine:

Sine = Perpendicular/Hypotenuse

Cosine:

Cosine = Base/Hypotenuse

Tangent:

Tangent = Perpendicular/Base

Secant:

Secant = Hypotenuse/Perpendicular

Cosecant:

Cosecant = Hypotenuse/Base

Cotangent:

Cotangent = Base/Perpendicular

Inverse SOHCAHTOA Ratios:

Arcsine:

Arcsin = sin^{-1}x

Arccosine:

Arccos = cos^{-1}x

Arctangent:

Arctan = tan^{-1}x

Arcsecant:

Arcsec = sec^{-1}x

Arccosecant:

Arccosecant = cosec^{-1}x

Arcotangent:

Arccotangent = cot^{-1}x

What Other Mnemonics Can You Use to Remember Trig Ratios of the Triangle?

Another most widely used sentence that help you recalling the trig functions as follows:

“Oscar Had A Heap Of Apples”

Which implies that:

Sin(θ) = Oscar / Had
Cos(θ) = A / Heap
Tan(θ) = Of / Apples

Illustrations:

For the triangle given as under, apply SOH CAH TOA find angle and side r:

Solution:

Here we have:

sin(20°) = 10/r

r{sin(20°)} = 10

r = 10/sin(20°)

r = 10/0.3420

r = 29.239

Now you must be thinking how to find angles using SOHCAHTOA. Let us guide you!

Angle 1 = 90°

Angle 2 = 20°

Angle 3 = ?

So we have:

Angle 3 = 90° – 20°

Angle 3 = 70°