Math: Trigonometry Deals with triangles and the relationships between the sides and angles of triangles. The sine function (sin), defined as the ratio of the side opposite the angle to the hypotenuse. The cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse. The tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg. SOHCAHTOA The trigonometric functions are periodic, with a period of 360 degrees or 2π radians. That means their values repeat at those intervals The complex function cis is particularly useful The law of sines (also know as the "sine rule") for an arbitrary triangle states: The law of cosines (also known as the cosine formula, or the "cos rule") is an extension of the Pythagorean theorem to arbitrary triangles: Law of Tangents: (a - b)/(a + b) = tan [(A-B)/2] / tan [(A+B)/2] The graphs of trigonometric functions have different wave patterns. The wave’s speed is called its frequency. The range of these numbers is the wave's amplitude. Ex: 2 sin(0.5A°), 2 is the amplitude, 0.5 is the frequency. Phase Shift: For example, the function f(x) = 3sin (x – π) has a phase shift of π. That is, the graph of f(x) = 3sin x is shifted π units to the right. Pythagorean theorem: c²=a² + b² A unit circle is a circle of radius one unit with its centre at the origin. Any radius of the unit circle is the hypotenuse of a right triangle that has a (horizontal) leg of length cos and a (vertical) leg of length sin . The angle is defined as the radius measured in standard position. Radians are another way to measure angles. A degree is equal to 1 /360 of a circle, while a radian is equal to the angle that intercepts an arc of the same length as the radius of the circle.