Solve both parts and justify the conditions used. Part A: Given an acute angle, find sin 2α. Part B: Find cos θ when θ is in quadrant II.

01 / Standard#Your turn

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

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

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

Hint 2

B: Use coordinates on the terminal ray and a positive radius.

Worked solution

Part A 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.
Part B 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.

A: The requested value is 0.96. B: The requested value is -0.8.

Checks and common pitfalls: The acute-angle condition selects the sign. The quadrant determines the negative cosine.

Reasoning checklist · self / teacher assessment

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

Trigonometric functions: mixed assessment