Algebra and Trigonometry

# Key Terms

amplitude
the vertical height of a function; the constant$A A$appearing in the definition of a sinusoidal function
arccosine
another name for the inverse cosine;$arccos x= cos −1 x arccos x= cos −1 x$
arcsine
another name for the inverse sine;$arcsin x= sin −1 x arcsin x= sin −1 x$
arctangent
another name for the inverse tangent;$arctan x= tan −1 x arctan x= tan −1 x$
inverse cosine function
the function$cos −1 x, cos −1 x,$which is the inverse of the cosine function and the angle that has a cosine equal to a given number
inverse sine function
the function$sin −1 x, sin −1 x,$which is the inverse of the sine function and the angle that has a sine equal to a given number
inverse tangent function
the function $tan −1 x, tan −1 x,$which is the inverse of the tangent function and the angle that has a tangent equal to a given number
midline
the horizontal line$y=D, y=D,$where$D D$appears in the general form of a sinusoidal function
periodic function
a function$f( x ) f( x )$that satisfies$f( x+P )=f( x ) f( x+P )=f( x )$for a specific constant$P P$and any value of$x x$
phase shift
the horizontal displacement of the basic sine or cosine function; the constant$C B C B$
sinusoidal function
any function that can be expressed in the form$f( x )=Asin( Bx−C )+D f( x )=Asin( Bx−C )+D$or$f( x )=Acos( Bx−C )+D f( x )=Acos( Bx−C )+D$