SOHCAHTOA & Trig on the New SAT
When students found out last year that trigonometry would be on the test, they let out a collective gasp that was heard on Mars. After all, trigonometry identities have been the bane of many novitiates since the time Euclid first wielded a protractor. To make matters worse many high school students planning to take the SAT had yet to take a trigonometry class.
While I’m not going to tell you that trigonometry is easy, or that the trigonometry on the SAT is going to be a cinch, the news isn’t as bad as you might think. First off, the trigonometry covered on the SAT will be relatively basic, encompassing two main areas: the unit circle and sine, cosine, and tangent.
The sin (π/2 – u) = cos u scary stuff will be absent. The test is more concerned with your understanding of basic concepts.
In this post, I’m going to focus on sine, cosine, and tangent, and how they relate to a triangle. To do so, I’m going to use one of the most important mnemonics, or memory device, you’ll ever learn:
To understand exactly what this means, let’s start with the following triangle.
Triangle ABC is a right triangle. Indeed, SOHCAHTOA only applies to right triangles. But let’s forget that funky mnemonic for a moment and discuss sine, cosine, and tangent. What exactly do these mean? Well, there are certain properties based on the relations of the sides of the triangle. To understand these properties, you’ll have to choose one of the angles that is not the right angle. I’ll choose angle ABC, which I’ll call Θ. The sine of Θ is the side opposite Θ divided by the hypotenuse (the longest side of a right triangle). To simplify:
Sine of Θ = Opposite/Hypotenuse, or AC/BC
The cosine of Θ equals the adjacent side, or the side right next to Θ that is not the hypotenuse (in this case AB), divided by the hypotenuse.
Cosine of Θ = Adjacent/Hypotenuse, or AB/BC
Finally, the tangent of Θ is the side opposite Θ divided by the adjacent side.
Tangent of Θ = Opposite/Adjacent, or AC/AB
That’s enough trigonometry for now. Check in next week, when we’ll present SOHCAHTOA: Part II!