Solve both parts and justify the conditions used. Part A: Two daily temperature observations fit a sinusoid. Explain why more observations are needed before predicting its period. Part B: Given an acute angle, find sin 2α.

01 / Standard#Your turn

\begin{gathered}\text{B: }\sin\alpha=3/5\end{gathered}

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

A: Define the geometric or periodic quantities with units, then choose a trigonometric relation.

Hint 2

B: Select an identity that matches the structure, retain signs and check denominators.

Worked solution

Part A reasoning
Define the geometric or periodic quantities with units, then choose a trigonometric relation.
Record enough observations over several cycles and compare a fitted curve with residual errors and context.
A visual fit alone does not establish a unique periodic model.
Part B reasoning
Select an identity that matches the structure, retain signs and check denominators.
Calculate or simplify this relation.
$\cos\alpha=4/5;\quad\sin2\alpha=2(3/5)(4/5)=24/25$
The acute-angle condition selects the sign.

A: Several amplitudes, phases and periods can fit two observations. B: The requested value is 0.96.

Checks and common pitfalls: A visual fit alone does not establish a unique periodic model. The acute-angle condition selects the sign.

Reasoning checklist · self / teacher assessment

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

Trigonometric functions: mixed assessment