Basic Trigonometry

Trigonometry is by definition the study of triangles, although there are other ideas involved with it. However, all concepts are derived from triangles. Basic trigonometry deals with six major functions, which are seen throughout the whole course. The six functions of trigonometry are sine, cosine, tangent, cosecant, secant, and cotangent. They are abbreviated as sin, cos, tan, csc, sec, and cot. Here's an example to explain how they work. Let's take a right triangle (it must be right), with sides 3, 4, and 5 (five is the hypotenuse). Choose the angle of elevation, and call it theta. Theta is the popular Greek letter assigned to unknown triangle angles. Here’s a picture to act as a visual aid. Please note, I drew it in MS Paint, it does not look good:



That horrible looking circle with the line represents theta. Sin is opposite over hypotenuse, and the opposite side from theta is 3, and the hypotenuse is 5. So, the sin of theta is 3/5. Cos is adjacent over hypotenuse, so that's 4/5. Tan is opposite over adjacent, so that's 3/4. Now, the other three are just reciprocals. Csc is the reciprocal of sin, so it's hypotenuse over opposite, making 5/3. Sec is reciprocal of cos, so it's 5/4. And cot is the reciprocal of tan, so that's 4/3. I've always thought sin should go with cos and sec should go with csc. Tan and cot are the only ones that make sense. To review:

Sin: opp/hyp
Cos: adj/hyp
Tan: opp/adj
Csc: hyp/opp
Sec: hyp/adj
Cot: adj/opp

Sine, cosine, tangent, cosecant, secant, and cotangent are used all throughout trig, so it's imperative that the functions be memorized.