Question Number 16855 by Tinkutara last updated on 27/Jun/17
$$\mathrm{If}\:\mathrm{sin}\:\theta\:=\:\frac{\mathrm{1}}{\mathrm{2}},\:\mathrm{cos}\:\phi\:=\:\frac{\mathrm{1}}{\mathrm{3}},\:\mathrm{then}\:\theta\:+\:\phi \\ $$ $$\mathrm{belongs}\:\mathrm{to},\:\mathrm{where}\:\mathrm{0}\:<\:\theta,\:\phi\:<\:\frac{\pi}{\mathrm{2}} \\ $$ $$\left(\mathrm{1}\right)\:\left(\frac{\pi}{\mathrm{3}},\:\frac{\pi}{\mathrm{2}}\right) \\ $$ $$\left(\mathrm{2}\right)\:\left(\frac{\pi}{\mathrm{2}},\:\frac{\mathrm{2}\pi}{\mathrm{3}}\right) \\ $$
Answered by ajfour last updated on 27/Jun/17
$$\:\frac{\pi}{\mathrm{3}}\:<\phi<\frac{\pi}{\mathrm{2}}\:\mathrm{and}\:\:\theta=\frac{\pi}{\mathrm{6}}\:\:\: \\ $$ $$\mathrm{so}\:\:\frac{\pi}{\mathrm{2}}<\theta+\phi\:<\:\frac{\mathrm{2}\pi}{\mathrm{3}}\:. \\ $$
Commented byTinkutara last updated on 27/Jun/17
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$