# Math: Trigonometry ```Math: Trigonometry
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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.
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The cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse.
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The tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.
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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
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The law of sines (also know as the &quot;sine rule&quot;) for an arbitrary triangle states:
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The law of cosines (also known as the cosine formula, or the &quot;cos rule&quot;) is an
extension of the Pythagorean theorem to arbitrary triangles:
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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&deg;), 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: c&sup2;=a&sup2; + b&sup2;
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