To define the trigonometric functions of an angle theta assign one of the angles in a right triangle that value. The functions sine, cosine, and tangent can all be defined by using properties of a right triangle. A right triangle has one angle that is 90 degrees. The longest side of the triangle is the hypotenuse. The side opposite theta will be referred to as opposite. The other side next to theta will be referred to as adjacent. The following properties exist:
[画像:definition of the sine function]
[画像:definition of the cosine function]
[画像:definition of the tangent function]
[画像:definition of the cosecant function]
[画像:definition of the secant function]
[画像:definition of the cotangent function]
unit circle definition for sine
unit circle definition for cosine
[画像:unit circle definition for tangent]
[画像:unit circle definition for cosecant]
[画像:unit circle definition for secant]
[画像:unit cirle definition for cotangent]
The possible angle input for each function is defined below:
domain of sine function
domain of cosine function
[画像:domain of tangent function]
domain of cosecant function
[画像:domain of secant function]
domain of cotanent function
The ranges of values possible for each of these functions are:
range of sine function
range of cosine function
range of tangent function
range of cosecant function
range of secant function
range of cotangent function
The periods for each of these trig functions are:
[画像:period of cosine function]
[画像:period of tangent function]
[画像:period of cosecant function]
[画像:period of secant function]
[画像:period of cotangent function]
The definitions of the inverse trig functions are:
definition of inverse sine
definition of inverse cosine
definition of inverse tangent
Inverse Trig functions are also notated as:
inverse notation of asin
inverse notation of acos
inverse notation of atan
domain of inverse sin
domain of inverse cosine
domain of inverse tangent
range of inverse sin
range of inverse cosine
