7.4 SAT Math - Trigonometry

YOU DO NOT NEED TRIGONOMETRY ON THE SATs!  Any problem on this test in which you may think you need trig can be solved a different way – through the Pythagorean Theorem, by remembering your special triangles relationships, etc.  So if you never learned trig or if you're awful at it, stop reading now.

That being said, if you're great at trig, there are times when you may find it faster and/or easier to just use trig on the SAT because it's closer to what you're studying now in school.  Even if you find that to be the case, the trig you might want to use on this test is very basic stuff.  Don't get fancy or pull out crazy theorems.  You don't need them and you will most definitely be making the math problem harder than it has to be by doing so.  The only trig you might use on this test has to do with right triangles and basic definitions:

Each of the definitions of those sides is in relation to , which means if the angle being discussed is in a different spot, the sides of that particular triangle will be different – the opposite side is always opposite the angle, the adjacent side always next to the angle.  The hypotenuse is always opposite the right angle, so that one won't change.

The easiest way to remember this relationships is through the acronym SOHCAHTOA (pronounced "so-kah-toe-ah").  This stands for Sin Opposite Hypotenuse, Cosine Adjacent Hypotenuse, Tangent Opposite Adjacent. 

-SAT Math Hint: Anytime you have a question on this test for which you think you're going to use trig, immediately write down "SOHCAHTOA" in the margin so that you have your relationships right in front of you.

Sine, cosine and tangent are all ratios of the sides to each other.  If you see that trig may be useful on a question, you will NOT be given all three sides, but will rather be given two sides and an angle and asked to solve the third, like this:

15. In triangle DEF above, what is the approximate length of side DE?

(A) .56
(B) .75
(C) 1.5
(D) 2.25
(E) 2.6

You can use a trig function here to solve for DE, keeping in mind that the side you need to solve for is the Opposite side to the known angle, so sine or tangent would be more useful than cosine.  The setup for that work would be:

From there, type "sin 30" or "tan 30" into your calculator, then multiply by the denominator to get DE.  Either way, you should end up with .75, or B).
-SAT Math Hint: Don't forget the other Geometry Rules!  Just by looking at this triangle, you should have eliminated C, D and E because the hypotenuse is always the longest side.  Without doing any work, you narrowed your chances of getting this one right to 50/50.

(If you don't like the trig, you could have used your special triangle rules here – it's a 30-60-90 triangle.  You could also have used the Pythagorean Theorem to solve.  There are often many different ways to solve a problem.  Use the first way you notice that you find quickest and easiest.)

One other trig rule that may be helpful is the Law of Sines:

This states that the ratio of the sine of an angle to its opposite side is always equal to the ratio of the sine of any other angle in that triangle to its opposite side.  The Law of Sines sets up the triangle like this:

Again, the Law of Sines is simply a shortcut you may find useful if you're comfortable with trig.  If not, memorize the special triangle rules and you should be fine.