$\Delta ABC$ is a right-angled triangle where $\angle ABC=90{}^\circ $. $BC$ is produced

Question

$\Delta ABC$ is a right-angled triangle where $\angle ABC=90{}^\circ $. $BC$ is produced to $D$ and $\tan \angle ACB=\frac{4}{3}$. Write down each of the following as a fraction, without the use of a calculator. $\sin \angle ACB$, $\cos \angle BAC$, $\cos \angle ACD$.

Accepted Answer

(i) $\frac{4}{5}$ (ii) $\frac{4}{5}$ (iii) $-\frac{3}{5}$

Trigonometry of Acute and Obtuse Angles: Evaluating Sines and Cosines.

Trigonometry of Acute and Obtuse Angles: Evaluating Sines and Cosines.

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