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SOHCAHTOA – What The Heck is That?

Ever heard of SOHCAHTOA?  Ring a bell at all?  It’s likely that you learned this as part of learning about trigonometry, which is basically the study of triangles the relationships between the sides and the angles in a triangle.

Sine, cosine, and tangent are just words that describe how sides of a right triangle relate to one another and the angles in the triangle.   Each of these simply defines a ratio.  The sine of one of the non-right angles in a right triangle is defined by taking the length of the side opposite the angle and dividing it by the length of the hypotenuse, or Sine = Opposite over the Hypotenuse.  Take the first letters of each of these and you have SOH.

Cosine is similar, except that it is CAH or Cosine = Adjacent over the Hypotenuse.

Tangent is TOA or Tangent = Opposite over the Adjacent.

Put them all together and you have SOH CAH TOA!

Let’s look at the following triangle:

The sine, cosine, and tangent for each of the angles other than the right angle are listed above.

This can help you find the length of sides, if you know some of the information about the lengths and angles.  For example, the sin of a 30° angle is ½ or 0.5.  If you know that the length of z (the hypotenuse) is 20 and you need to find the length of y, then use the sin formula.  sin(30) = y/z or 0.5 = y/20.  That simplifies to 20(0.5) = y or y = 10.  Very handy when you know some of the basic sin and cos and tan values.

Here are some easy sin/cos/tan values that will come in handy on the ACT Test:

sin(30) = 0.5

cos(60) = 0.5

sin(0) = 0

sin(90) = 1

cos (0) = 1

cos (90) = 0

tan (0) = 0

tan (90) = undefined

There are some others (like sin of 60), but those are a bit harder to remember and we’ll leave them for a later discussion.


For more ACT Math Test help, make sure that you get ACT Exam Secrets.

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