Basic Trigonometry of the Right Triangle - SAT and ACT Prep

Right Triangle Trigonometry

Today I would like to begin talking about right triangle trigonometry. If you will be taking the ACT or one of the SAT math subject tests, and you are going for a very high score, then it is important that you understand the material covered here.

Let’s begin by focusing on angle A in the following picture:

Note that the hypotenuse is ALWAYS the side opposite the right angle.

The other two sides of the right triangle, called the legs, depend on which angle is chosen. In this picture we chose to focus on angle A. Therefore the opposite side is BC, and the adjacent side is AC.

Now you should simply memorize how to compute the six trig functions:

Here are a couple of tips to help you remember these:

(1) Many students find it helpful to use the word SOHCAHTOA. You can think of the letters here as representing sin, opp, hyp, cos, adj, hyp, tan, opp, adj.

(2) The three trig functions on the right are the reciprocals of the three trig functions on the left. In other words, you get them by interchanging the numerator and denominator. It’s pretty easy to remember that the reciprocal of tangent is cotangent. For the other two, just remember that the “s” goes with the “c” and the “c” goes with the “s.” In other words, the reciprocal of sine is cosecant, and the reciprocal of cosine is secant.

Note that if you are preparing for the ACT or Level 1 SAT math subject test, then it is not that important for you to know the reciprocal trig functions given in the right hand column, but it also couldn’t hurt to be somewhat familiar with them.