Maths Extension 1 Year 12 - Inverse Trigonometric Functions - Lesson 2
Graphs of Inverse Trig Functions
Name
Date
Class
1. Lesson focus
Graphs of inverse trigonometric functions. Inverse trig graphs follow principal ranges: arcsin and arctan increase, while arccos decreases; endpoints and horizontal asymptotes depend on the function.
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. Find the intercepts of y=arccos x.
3. Describe the end behaviour of y=arctan x.
3. Challenge
Solve arccos x=2π/3.
4. Multiple choice
Which point is on y=arcsin x?
A. (0,π/2)
B. (1,0)
C. (−1,−π/2)
D. (−1,π/2)
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. State the domain and range of y=arcsin x.
Domain [−1,1]; range [−π/2,π/2].
2. Find the intercepts of y=arccos x.
x-intercept: arccos x=0 gives x=1, so (1,0). y-intercept: x=0 gives (0,π/2).
3. Describe the end behaviour of y=arctan x.
As x→−∞, y→−π/2; as x→∞, y→π/2. These are horizontal asymptotes.
Challenge. Solve arccos x=2π/3.
Cosine both sides: x=cos(2π/3)=−1/2, which lies in the domain [−1,1].
Multiple choice. Which point is on y=arcsin x?
Correct answer: C. arcsin(−1)=−π/2, so (−1,−π/2) lies on this graph; the other ordered pairs do not match the principal arcsin values.
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