Inverse Trigonometric Functions: Definitions, Graphs, and Calculations in Precalculus
Studied by 1 person
Call Kai
Learn
Practice Test
Spaced Repetition
Match
Flashcards
Knowt Play1/19
There's no tags or description
Looks like no tags are added yet.
Name | Mastery | Learn | Test | Matching | Spaced |
|---|
No study sessions yet.
20 Terms
What is the inverse cosine function denoted by?
It is denoted by cos⁻¹ or arccos.
On which interval is the cosine function one-to-one?
The interval [0, π].
What is the inverse tangent function denoted by?
It is denoted by tan⁻¹ or arctan.
On which interval is the tangent function restricted to define its inverse?
The interval (-π/2, π/2).
What are the three most common inverse trigonometric functions?
Inverse sine (sin⁻¹), inverse cosine (cos⁻¹), and inverse tangent (tan⁻¹).
What is the domain of the inverse sine function?
The domain is [-1, 1].
What is the range of the inverse sine function?
The range is [-π/2, π/2].
What is the domain of the inverse cosine function?
The domain is [-1, 1].
What is the range of the inverse cosine function?
The range is [0, π].
What is the domain of the inverse tangent function?
The domain is all real numbers.
What is the range of the inverse tangent function?
The range is (-π/2, π/2).
How do you evaluate an inverse trigonometric function?
Determine the angle whose trigonometric function gives the specified value.
What happens if you input a value outside the domain of an inverse trigonometric function? (answer: error message:
The calculator will display an error message.
What mode should a calculator be in to evaluate inverse trigonometric functions?
The calculator should be in radian mode.
What is the approximate value of sin⁻¹(0.5)?
π/6 or 30 degrees.
What is the approximate value of cos⁻¹(0)?
π/2 or 90 degrees.
What is the approximate value of tan⁻¹(1)?
π/4 or 45 degrees.
What is the significance of the range in inverse trigonometric functions?
The range defines the output values for the inverse functions.
Why is it necessary to restrict the domain of trigonometric functions to define their inverses?
To ensure that the function is one-to-one and has an inverse.
What is a one-to-one function?
A function where no two different input values can produce the same output value.
Real-life examples include people and their unique passport numbers, or a student and their assigned student ID. Each person has only one passport, and each passport belongs to only one person.