Solve both parts and justify the conditions used. Part A: Evaluate without a calculator. Part B: How many coterminal representatives of 30° lie in this closed interval?

01 / Standard#Your turn

\begin{gathered}\text{A: }\sin(\pi)+\sin(0)\\\text{B: }[-3240^{\circ},3240^{\circ}]\end{gathered}

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

A: Use unit-circle symmetry and periodicity; determine the sign before simplifying.

Hint 2

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

Worked solution

Part A reasoning
Use unit-circle symmetry and periodicity; determine the sign before simplifying.
Calculate or simplify this relation.
$\sin(\pi)+\sin(0)=0$
The sine coordinate is zero at integer multiples of π.
Part B reasoning
Keep degrees and radians distinct and use the definition of angular measure.
Calculate or simplify this relation.
$-3240\le30+360n\le3240\Rightarrow -9\le n\le8$
Integer n must satisfy both bounds.

A: The requested value is 0. B: The requested value is 18.

Checks and common pitfalls: The sine coordinate is zero at integer multiples of π. Integer n must satisfy both bounds.

Reasoning checklist · self / teacher assessment

Think first. Reveal a hint when the class is ready.

Trigonometric functions: mixed assessment