Solve both parts and justify the conditions used. Part A: Find cos θ when θ is in quadrant II. Part B: Two daily temperature observations fit a sinusoid. Explain why more observations are needed before predicting its period.

01 / Foundation#Your turn

\begin{gathered}\text{A: }\sin\theta=3/5\end{gathered}

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.
$\cos^2\theta=1-9/25=16/25;\quad\cos\theta=-4/5$
The quadrant determines the negative cosine.
Part B 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.

A: The requested value is -0.8. B: Several amplitudes, phases and periods can fit two observations.

Checks and common pitfalls: The quadrant determines the negative cosine. A visual fit alone does not establish a unique periodic model.

Reasoning checklist · self / teacher assessment

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

Trigonometric functions: mixed assessment