Question

If sin $\theta$ =$\frac{a}{b}$ then cos $\theta$ = ?

(a) $\frac{b}{\sqrt{b^2-a^2}}$(b) $\frac{\sqrt{b^2-a^2}}{b}$(c) $\frac{a}{\sqrt{b^2-a^2}}$ (d) $\frac{b}{a}$

Answer 1

sin $\theta$ =$\frac{a}{b}$

$\therefore cos\theta =\sqrt{(1-si{n}^2\theta )}[\because si{n}^2\theta +co{s}^2\theta =1]$

or, $cos\theta =\sqrt{(1-\frac{a^2}{b^2})}$

or, $cos\theta =\sqrt{\frac{(b^2-a^2)}{b^2}}$

or, $cos\theta =\frac{\sqrt{(b^2-a^2)}}{b}$