Inverse Trigonometric Functions - Sharp EL-9600 User Manual

Chapter five
INVERSE TRIGONOMETRIC
FUNCTIONS
Introducing the Topic
In this chapter, you and your students will learn how to compute and graph
inverse trigonometric functions. The inverse is found by interchanging the
range and domain of the trigonometric function. Thus, the domain of the
trigonometric function becomes the range of the inverse and the range of the
trigonometric function becomes the domain of the inverse.
For example, the sine function has IR as its domain and - 1
Therefore, the inverse of the sine function (arcsine or inverse sine) will have
- 1
x 1 as its domain and IR as its range. Notice, like some algebraic functions,
the inverse of trigonometric function will not be a function. This is due to
periodicity of the trigonometric function's domain extends to the inverse's
range. Thus, one value in the inverse's domain will correspond to more than
one value in the inverse's range. To make the inverse a function, you will limit
the domain of the trigonometric function so it forms a one-to-one function.
Limit the domain of the sine and tangent functions to - /2
cosine function to 0
whose inverses are functions. The values within these limited domains are called
the principal values. Notations for "inverse sine" are "arcsin" and "sin
Inverse Trigonometric Functions/TRIGONOMETRY USING THE SHARP EL-9600
x . These limited domains result in one-to-one functions
y 1 as its range.
x /2, and limit the
–1
".
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