Solve both parts and justify the conditions used. Part A: Determine whether the two claimed trigonometric values can occur together. Part B: A wheel has radius 8 m and its centre is 10 m above ground. Find the greatest passenger height.
- Use the domain, units and sampling assumptions stated in the question.
- Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons
Working and explanation
BUILD THE REASONING
Hint 1
A: Use coordinates on the terminal ray and a positive radius.
Hint 2
B: Define the geometric or periodic quantities with units, then choose a trigonometric relation.
Worked solution
Part A reasoning
Use coordinates on the terminal ray and a positive radius.
Calculate or simplify this relation.
Each value being individually between −1 and 1 is insufficient.
Part B reasoning
Define the geometric or periodic quantities with units, then choose a trigonometric relation.
Calculate or simplify this relation.
The corresponding minimum is 2 m, so the wheel remains above ground.
A: No, because their squared sum is not one. B: The requested value is 18.
Checks and common pitfalls: Each value being individually between −1 and 1 is insufficient. The corresponding minimum is 2 m, so the wheel remains above ground.
Reasoning checklist · self / teacher assessment
- Solve part A with its stated restrictions.
- Solve part B using an appropriate representation.
- Give the reasoning and check conditions in both parts.
Think first. Reveal a hint when the class is ready.