Note: This is the Solution of review exercise 6.2 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 6.2
Question # 01: For each of the following right-angles triangles, find the trignometric ratios:
\((i)\) \(\quad\) \( \sin \theta\)
\((ii)\) \(\quad\) \(\cos \theta \)
\((iii)\) \(\quad\) \(\tan \theta \)
\((iv)\) \(\quad \)\(\sec \theta \)
\((v)\) \(\quad \) \(\csc \theta \)
\((vi)\) \(\quad \) \(\cot\phi \)
\((vii)\) \(\quad \) \(\tan \phi \)
\((viii)\) \(\quad \) \(\csc \phi \)
\((ix)\) \(\quad \) \(\sec \phi \)
\((x)\) \(\quad \) \(\cos \phi \)
Question 2: For the following right-angled triangle \(\small{ABC}\) find the trignometric ratios for which \(\small{m\angle A =\phi}\) and \(\small{m\angle C=\theta}\)
\((i)\) \(\quad\) \( \sin \theta\)
\((ii)\) \(\quad\) \(\cos \theta \)
\((iii)\) \(\quad\) \(\tan \theta \)
\((vi)\) \(\quad \) \(\sin \phi \)
\((vii)\) \(\quad \) \(\cos \phi \)
\((viii)\) \(\quad \) \(\tan \phi \)
Question 3: Consider the adjoining triangle \(\small{ABC}\), verify that:
\((i)\) \(\quad\) \( \sin \theta \csc \theta =1\)
\((i)\) \(\quad\) \( \cos \theta \sec \theta =1\)
\((iii)\) \(\quad\) \( \tan \theta \cot \theta =1\)
Question 4: Fill in the blanks.
\((i)\) \(\quad\) \( \sin 30^\circ = \sin (90^\circ\ -\ 60^\circ)=\_\_\_\_\_\)
\((ii)\) \(\quad\) \( \cos 30^\circ = \cos (90^\circ\ -\ 60^\circ)=\_\_\_\_\_\)
\((iii)\) \(\quad\) \( \tan 30^\circ = \tan (90^\circ\ -\ 60^\circ)=\_\_\_\_\_\)
\((iv)\) \(\quad\) \( \tan 60^\circ = \tan (90^\circ\ -\ 30^\circ)=\_\_\_\_\_\)
\((v)\) \(\quad\) \( \sin 60^\circ = \sin (90^\circ\ -\ 30^\circ)=\_\_\_\_\_\)
\((vi)\) \(\quad\) \( \cos 60^\circ = \cos (90^\circ\ -\ 30^\circ)=\_\_\_\_\_\)
\((vii)\) \(\quad\) \( \sin 45^\circ = \sin (90^\circ\ -\ 45^\circ)=\_\_\_\_\_\)
\((viii)\) \(\quad\) \( \tan 45^\circ = \tan (90^\circ\ -\ 45^\circ)=\_\_\_\_\_\)
Question 5: In a right angled triangle \(\small{ABC}\), \(\small{m\angle B =90^\circ}\) and \(\small{C}\) is an acute angle of \(60^\circ\). Also \(\small{\sin \angle A =\frac{a}{b}}\), then find the following trignometric ratios:
\((i)\) \(\quad\) \( \frac{m\overline{BC}}{m\overline{AB}}\)
\((ii)\) \(\quad\) \( \cos 60^\circ\)
\((iii)\) \(\quad\) \( \tan 60^\circ\)
\((iv)\) \(\quad\) \( \csc \frac{\pi}{3}\)
\((v)\) \(\quad\) \( \cot 60^\circ\)
\((vi)\) \(\quad\) \( \sin 30^\circ\)
\((vii)\) \(\quad\) \( \cos 30^\circ\)
\((viii)\) \(\quad\) \( \tan \frac{\pi}{6}\)
\((ix)\) \(\quad\) \( \sec 30^\circ\)
\((x)\) \(\quad\) \( \cot 30^\circ\)