Maths Extension 1 Year 12 - Inverse Trigonometric Functions - Lesson 1
Inverse Trigonometric Functions
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Date
Class
1. Lesson focus
Principal values and domains of inverse trigonometric functions. Principal ranges are arcsin:[−π/2,π/2], arccos:[0,π], arctan:(−π/2,π/2); inputs must lie in each function’s domain.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. Evaluate arccos(−√2/2).
3. State the domain and range of arctan x.
3. Challenge
Solve arctan x=π/6.
4. Multiple choice
Which is the range of arccos x?
A. [−π/2,π/2]
B. [0,π]
C. (−π/2,π/2)
D. [0,2π)
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Evaluate arcsin(−1/2).
The principal angle in [−π/2,π/2] with sine −1/2 is −π/6.
2. Evaluate arccos(−√2/2).
The principal angle in [0,π] is 3π/4.
3. State the domain and range of arctan x.
Domain: all real x. Range: (−π/2,π/2).
Challenge. Solve arctan x=π/6.
Take tangent: x=tan(π/6)=1/√3=√3/3.
Multiple choice. Which is the range of arccos x?
Correct answer: B. By definition the principal arccos angle lies in [0,π].
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