Key Terms

amplitude

the vertical height of a function; the constant $A$ appearing in the definition of a sinusoidal function

arccosine

another name for the inverse cosine; $\arccos x={\cos }^{-1}x$

arcsine

another name for the inverse sine; $\arcsin x={\sin }^{-1}x$

arctangent

another name for the inverse tangent; $\arctan x={\tan }^{-1}x$

inverse cosine function

the function ${\cos }^{-1}x,$ 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 ${\sin }^{-1}x,$ 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 ${\tan }^{-1}x,$ which is the inverse of the tangent function and the angle that has a tangent equal to a given number

midline

the horizontal line $y=D,$ where $D$ appears in the general form of a sinusoidal function

periodic function

a function $f\left(x\right)$ that satisfies $f\left(x+P\right)=f\left(x\right)$ for a specific constant $P$ and any value of $x$

phase shift

the horizontal displacement of the basic sine or cosine function; the constant $\frac{C}{B}$

sinusoidal function

any function that can be expressed in the form $f\left(x\right)=A\sin \left(Bx-C\right)+D$ or $f\left(x\right)=A\cos \left(Bx-C\right)+D$