The subject matter of a trigonometry course typically entails these concepts: angle measurement, trigonometric functions, magic identity, addition formulas, double-angle and half-angle formulas, product and sum formulas, trigonometric equations and the table of trigonometric identities. The table of trigonometric identities visually depicts all of the trigonometric functions and their relationships to one another. Other higher-level trigonometry classes involve derivatives of trigonometric identities (calculus) and hyperbolic trigonometry.
The most common phrase heard in a trigonometry class will most likely be "soa cah tao," an artificial construction that represents the relationship between trigonometric functions. "Soa" refers to the equation for sine: sine equals the opposite side divided by the adjacent side. "Cah" refers to the fact that cosine equals the adjacent side divided by the hypotenuse. "Toa" refers to the fact that the tangent equals the opposite side divided by the adjacent side. These relationships are the foundation of trigonometry.
Trigonometry is particularly concerned with right triangles, and the relationships between side lengths and angles. Trigonometry uses one angle to find the angles and lengths of other sides, and this involves determining the hypotenuse of the triangle. Many equations that find the hypotenuse of a triangle use the equations for circles to find the answer. As a result, a lot of trigonometry uses circular equations and situates right triangles within a circular diagram.
Graphing also plays a large role in trigonometry. Students often use a graphing calculator or a computer to graph sine, cosine, tangent and cotangent. Cotangent is a trigonometric function used in equations to find the inverse of the tangent. The opposite of a sine graph is an inverted cosine graph. The opposite of a cosine graph is an inverted sine graph. The tangent's opposite graph is the cotangent graph, and the cotangent's opposite graph is the tangent's graph. The graphs for sine and cosine look like a wave, while the graphs of tangent and cotangent look like a vertical series of crooked lines.