The diagram below shows the chords $PQ$ and $RS$ and they intersect at the point $X$. Given th

Question

The diagram below shows the chords $PQ$ and $RS$ and they intersect at the point $X$. Given that $PQ=7$ cm, $RS=24$ cm, $\angle RXQ=90{}^\circ$ and $\angle PRS=\theta$ where $\theta$ varies. Prove that $PR = 24 \cos \theta + 7 \sin \theta$. Express $PR$ in the form $R \cos(\theta - \alpha)$. Find the maximum length of $PR$ and the corresponding value of $\theta$.

Accepted Answer

(a) $PR=24\cos\theta+7\sin\theta$ (b) $PR=25\cos(\theta-16.3^\circ)$ (c) $PR_{\max}=25\text{ cm}$ when $\theta=16.3^\circ$

Trigonometry - R-Formula and Trigonometric Extrema

Trigonometry - R-Formula and Trigonometric Extrema

Video Solution:

Solution:

Solution locked