Solve both parts and justify the conditions used. Part A: Is sine increasing on the whole real line? Give a counterexample. Part B: Write the angle as cπ radians; find c.

01 / Standard#Your turn

Solve both parts and justify the conditions used. Part A: Is sine increasing on the whole real line? Give a counterexample. Part B: Write the angle as cπ radians; find c.

\begin{gathered}\text{A: }y=\sin x\\\text{B: }210^{\circ}\end{gathered}

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: Read amplitude, period and allowed intervals directly from the trigonometric graph.

Hint 2

B: Keep degrees and radians distinct and use the definition of angular measure.

Worked solution

Part A reasoning
Read amplitude, period and allowed intervals directly from the trigonometric graph.
Calculate or simplify this relation.
$\sin(\pi/2)=1>0=\sin\pi$
Monotonicity must be specified on suitable intervals.
Part B reasoning
Keep degrees and radians distinct and use the definition of angular measure.
Calculate or simplify this relation.
$210^{\circ}\cdot\frac{\pi}{180^{\circ}}=\frac{7}6\pi$
The numerical coefficient changes with the unit, but the geometric angle does not.

A: No: π/2<π but sin(π/2)>sin π. B: The requested value is 1.16666667.

Checks and common pitfalls: Monotonicity must be specified on suitable intervals. The numerical coefficient changes with the unit, but the geometric angle does not.

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.

Solve both parts and justify the conditions used. Part A: Is sine increasing on the whole real line? Give a counterexample. Part B: Write the angle as cπ radians; find c.

Trigonometric functions: mixed assessment

What you will be able to explain

Try it. Leave your reasoning visible.

Solve both parts and justify the conditions used. Part A: Is sine increasing on the whole real line? Give a counterexample. Part B: Write the angle as cπ radians; find c.

Question sequence

Board plan

Anticipated thinking

Assessment checklist