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Precalculus: Trigonometric Functions

Terms and Formulae

Trigonometric Functions

Angles

Terms

Amplitude  -  One-half the distance between the minimun and maximum value of a periodic function.
Coterminal  -  Having the same terminal side (a property of angles).
Identity  -  An equation containing one or more trigonometric functions which are true regardless of the angle used.
Initial Side  -  The side of an angle from which the rotation begins, or the initial position of the ray whose rotation creates the angle.
Inverse Trigonometric Function  -  The inverses of the six trigononometric functions with specific restricted ranges. They are arcsine, arccosine, arctangent, arccosecant, arcsecant, and arccotangent.
Period  -  The repeating interval of a periodic function; the period of a function is a real number.
Quadrant  -  One of the four regions in the coordinate plane created by the intersection of the axes.
Quadrantal Angle  -  An angle in standard position whose terminal side lies along one of the axes.
Radian  -  A unit of measure for angles. One revolution equals 2Π radians. A radian is also the measure of the central angle that intercepts an arc of the same length as the radius.
Reference Angle  -  The positive acute angle formed between the terminal side of an angle and the x-axis.
Standard Position  -  The location of an angle such that its vertex lies at the origin and its initial side lies along the positive x-axis.
Terminal Side  -  The side of an angle after rotation; the final position of the ray whose rotation created an angle.
Trigonometric Functions  -  Sine, cosine, tangent, cosecant, secant, and cotangent are the six trigonometric functions.
Vertex  -  The common endpoint of two rays that form an angle.

Formulae

 
arccosecant y = arccsc(x) = csc -1(x) . Another way to write x = csc(y) .
 
arccosine y = arccos(x) = cos -1(x) . Another way to write x = cos(y) .
 
arccotangent y = arccot(x) = cot -1(x) . Another way to write x = cot(y) .
 
arcsecant y = arcsec(x) = sec -1(x) . Another way to write x = sec(y) .
 
arcsine y = arcsin(x) = sin -1(x) . Another way to write x = sin(y) .
 
arctangent y = arctan(x) = tan -1(x) . Another way to write x = tan(y) .
 
Cosecant Given a point P(x, y) on the terminal side of an angle θ in standard position, distance d from the origin, its cosecant is csc(θ) = = .
 
Cosine Given a point P(x, y) on the terminal side of an angle θ in standard position distance d from the origin, its cosine is cos(θ) = .
 
Cotangent Given a point P(x, y) on the terminal side of an angle θ in standard position, its cotangent is cot(θ) = = .
 
Secant Given a point P(x, y) on the terminal side of an angle θ in standard position, distance d from the origin, its secant is sec(θ) = = .
 
Sine Given a point P(x, y) on the terminal side of an angle θ in standard position, distance d from the origin, its sine is sin(θ) = .
 
Tangent Given a point P(x, y) on the terminal side of an angle θ in standard position, its tangent is tan(θ) = = .

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