With A=45° and cos C=4/5, calculate sin(2B).

01 / Standard#Your turn

Official paper · jm01-2025 · II.3(b) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Express B using the other two angles.

Hint 2

Use sin(2B)=−cos(2C).

Worked solution

Double B=π−A−C.
$2B=\frac{3\pi}2-2C,\quad\sin2B=-\cos2C$
Substitute the known cosine into the double-angle identity.
$\sin2B=1-2\cos^2C=1-2\left(\frac45\right)^2=-\frac7{25}$

sin(2B)=−7/25.

Checks and common pitfalls: The factor 2 in 1−2cos²C must be retained.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Double B=π−A−C.
$2B=\frac{3\pi}2-2C,\quad\sin2B=-\cos2C$
Substitute the known cosine into the double-angle identity.
$\sin2B=1-2\cos^2C=1-2\left(\frac45\right)^2=-\frac7{25}$

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

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