Note: This is the Solution of review exercise 6.4 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 6.4
Question # 01: Find the value of the following trigonometric ratios without using the calculator.
\((i)\) \(\quad\) \( \sin 30^\circ\)
\((ii)\) \(\quad\) \(\cos 30^\circ\)
\((iii)\) \(\quad\) \(\tan \frac{\pi}{6} \)
\((iv)\) \(\quad \)\(\tan 60^\circ \)
\((v)\) \(\quad \) \(\sec 60^\circ \)
\((vi)\) \(\quad \) \(\cos \frac{\pi}{3} \)
\((vii)\) \(\quad \) \(\cot 60^\circ \)
\((viii)\) \(\quad \) \(\sin 60^\circ \)
\((ix)\) \(\quad \) \(\sec 30^\circ \)
\((x)\) \(\quad \) \(\csc 30^\circ \)
\((xi)\) \(\quad \) \(\sin 45^\circ \)
\((xii)\) \(\quad \) \(\cos \frac{\pi}{4} \)
Question 2: Evaluate:
\((i)\) \(\quad\) \( 2\sin 60^\circ \cos 60^\circ\)
\((ii)\) \(\quad\) \(2\cos \frac{\pi}{3}\sin \frac{\pi}{3}\)
\((iii)\) \(\quad\) \(2 \sin 45^\circ +2\cos 45^\circ \)
\((iv)\) \(\quad \)\(\sin 60^\circ \cos 30^\circ +\cos 60^\circ \sin 30^\circ \)
\((v)\) \(\quad \) \(\cos 60^\circ \cos 30^\circ – \sin 60^\circ \sin 30^\circ \)
\((vi)\) \(\quad \) \(\sin 60^\circ \cos 30^\circ – \cos 60^\circ \sin 30^\circ \)
\((vii)\) \(\quad \) \(\cos 60^\circ \cos 30^\circ + \sin 60^\circ \sin 30^\circ \)
\((viii)\) \(\quad \) \(\tan \frac{\pi}{6}\cot \frac{\pi}{6}+1 \)
Question 3: If \(\sin \frac{\pi}{4 }\) and \(\cos \frac{\pi}{4}\) equal to \(\frac{1}{\sqrt{2}}\) each, then find the value of the followings:
\((i)\) \(\quad\) \( 2\sin 45^\circ -2 \cos 45^\circ\)
\((ii)\) \(\quad\) \(3 \cos 45^\circ +4\sin 45^\circ \)
\((iii)\) \(\quad \)\(5\cos 45^\circ -3 \sin 45^\circ \)