How to Use SOHCAHTOA? Tips and Examples

How to use SOHCAHTOA? In trigonometry, the study of right triangles begins. The three main trig functions (sine, cosine, and tangent) and their reciprocals (cosecant, secant, and cotangent) tell you something about the sides of a right triangle containing a given acute angle.

The diagonal side of this right triangle (or any right triangle) is called the hypotenuse. The 3-unit side of the triangle is called the opposite side since it is on the opposite side of the triangle from angle x. The side of length 4 is called the adjacent side because it’s adjacent to, or touches, angle x.

You can remember the definitions of sine, cosine, and tangent functions by using the mnemonic SohCahToa. SohCahToa uses the initial letters of sine, cosine, and tangent, and the initial letters of hypotenuse, opposite, and adjacent, to help you recall the following definitions. (To remember how to spell SohCahToa, note its pronunciation and that it consists of three groups of three letters each.)

What Trigonometry Concepts Are on the SAT?

There are two main types of trigonometry questions on the SAT. When you study both types of questions, you will have a good chance of succeeding on this part of the test.

In the first variety of questions, students must find the sine, cosine, or tangent of an angle using the sides of a triangle. In the second question type, students will need to determine an angle’s sine, cosine, or tangent by using the sine, cosine, or tangent of another angle. In both cases, students can use the acronym SOHCAHTOA to ensure that they answer the questions correctly.

Trigonometric Functions

In trigonometry, sine, cosine, and tangent are the three main functions. Based on a right triangle, all of them are derived from ratios. We need to label a right triangle before we can understand what ratios work for what function.

The opposite side is the side opposite to the angle in question. An adjacent side is the side next to the angle in question, and the hypotenuse is the longest side of a right triangle. Right angles always face the hypotenuse.

You can determine the sine, cosine, and tangent of a right triangle using the following ratios:

• An angle’s sine is equal to the side opposite the angle divided by the hypotenuse.
• An angle’s cosine is equal to the side adjacent to the hypotenuse divided by the angle.
• Tangent is equal to the side opposite the angle divided by the side adjacent to the angle.

SOHCAHTOA

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

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

Using these properties, you can solve almost any problem related to finding a right triangle’s side length or angle measure. SohCahToa can guarantee that you won’t make a mistake.

Tips for Using SOHCAHTOA

Still not quite sure how to use SOHCAHTOA? Here are some tips.

Remember the Correct Order

It’s easy to use SOHCAHTOA, but you need to make sure you’re using it correctly. If you get any of the letters mixed up, you will be unable to apply the formula correctly.

The following tongue twisters will help you remember SOHCAHTOA:

• Until old age, sailors often have curly auburn hair.
• Horses can always hear their owners approaching.
• One of the Old Hens caught another hen taking one away.

Write down the Formula

Whether you’re studying for the SAT or just practicing trigonometry on your homework, writing down SOHCAHTOA will help you remember how to use it. That way, you won’t get mixed up!

Identify Your Sides First

It can be difficult to remember which side is opposite and which side is adjacent. Before you begin working, identify each side and write it on your paper so you don’t make any careless mistakes.

Final Thoughts

What’s the SOHCAHTOA meaning? The SOHCAHTOA mnemonic helps you remember how to calculate the sides and angles of right triangles. You can prepare for your SAT or ACT by brushing up on the SOH CAH TOA formula and practicing SOH CAH TOA problems.