Question Number 166186 by mkam last updated on 14/Feb/22
$${if}\:{sin}\theta\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:{find}\:{cos}\theta \\ $$
Answered by pnuvu last updated on 14/Feb/22
$$\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$
Answered by MJS_new last updated on 15/Feb/22
$$\mathrm{cos}\:\theta\:=\pm\sqrt{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:\theta} \\ $$$$\mathrm{sin}\:\theta\:=\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\:\mathrm{cos}\:\theta\:=\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{or} \\ $$$$\mathrm{for}\:\mathrm{0}°\leqslant\theta<\mathrm{360}°: \\ $$$$\mathrm{sin}\:\theta\:=\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\:\theta=\mathrm{30}°\vee\theta=\mathrm{150}° \\ $$$$\Rightarrow\:\mathrm{cos}\:\theta\:=\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$