A,B lie in quadrant II, with sin A=2/5 and sin B=4/5. Find sin(A+B).

01 / Standard#Your turn

Official paper · jm01-2023 · I.13 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Both cosines are negative.

Hint 2

Use the sine addition formula.

Worked solution

Determine the cosines with the quadrant signs.
$\cos A=-\sqrt{21}/5,\quad\cos B=-3/5$
Substitute into the addition formula.
$\sin(A+B)=\frac25\left(-\frac35\right)+\left(-\frac{\sqrt{21}}5\right)\frac45=\frac{-6-4\sqrt{21}}{25}$

Checks and common pitfalls: Positive sine does not imply positive cosine in quadrant II.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Determine the cosines with the quadrant signs.
$\cos A=-\sqrt{21}/5,\quad\cos B=-3/5$
Substitute into the addition formula.
$\sin(A+B)=\frac25\left(-\frac35\right)+\left(-\frac{\sqrt{21}}5\right)\frac45=\frac{-6-4\sqrt{21}}{25}$

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

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