Terms and Formulae
Terms
Amplitude
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One-half the distance between the minimun and maximum value of a periodic
function.
Coterminal
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Having the same terminal side (a property of angles).
Identity
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An equation containing one or more trigonometric functions which are true
regardless of the angle used.
Initial Side
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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
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The inverses of the six trigononometric
functions with specific restricted ranges. They are arcsine,
arccosine, arctangent, arccosecant, arcsecant, and
arccotangent.
Period
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The repeating interval of a periodic function;
the period of a function is a real number.
Quadrant
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One of the four regions in the coordinate plane created by the intersection of
the axes.
Quadrantal Angle
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An angle in standard position whose terminal side lies along one of the
axes.
Radian
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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
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The positive acute angle formed between the terminal side of an angle and
the x-axis.
Standard Position
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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
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The side of an angle after rotation; the final position of the ray whose
rotation created an angle.
Trigonometric Functions
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Sine, cosine, tangent, cosecant, secant, and cotangent
are the six trigonometric functions.
Vertex
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The common endpoint of two rays that form an angle.
Formulae
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arccosecant
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y = arccsc(x) = csc-1(x). Another way to write x = csc(y).
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arccosine
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y = arccos(x) = cos-1(x). Another way to write x = cos(y).
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arccotangent
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y = arccot(x) = cot-1(x). Another way to write x = cot(y).
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arcsecant
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y = arcsec(x) = sec-1(x). Another way to write x = sec(y).
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arcsine
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y = arcsin(x) = sin-1(x). Another way to write x = sin(y).
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arctangent
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y = arctan(x) = tan-1(x). Another way to write x = tan(y).
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Cosecant
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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) = = .
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Cosine
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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) = .
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Cotangent
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Given a point P(x, y) on the terminal side of an angle θ in
standard position, its cotangent is cot(θ) = = .
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Secant
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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) = = .
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Sine
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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) = .
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Tangent
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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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