determiner-la-valeur-exacte-de-sin-85-4-

Question Number 73608 by mathocean1 last updated on 13/Nov/19

determiner la valeur exacte de sin(((85Π)/4))

$$\:\mathrm{determiner} \\ $$$$\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{exacte}\:\mathrm{de}\:\mathrm{sin}\left(\frac{\mathrm{85}\Pi}{\mathrm{4}}\right) \\ $$$$ \\ $$

Commented by mathmax by abdo last updated on 13/Nov/19

sin(((85π)/4)) =sin(20π +((5π)/4)) =sin(((5π)/4)) =sin(π +(π/4)) (20π is period) =−sin((π/4))=−((√2)/2)

$${sin}\left(\frac{\mathrm{85}\pi}{\mathrm{4}}\right)\:={sin}\left(\mathrm{20}\pi\:+\frac{\mathrm{5}\pi}{\mathrm{4}}\right)\:={sin}\left(\frac{\mathrm{5}\pi}{\mathrm{4}}\right)\:={sin}\left(\pi\:+\frac{\pi}{\mathrm{4}}\right)\:\:\left(\mathrm{20}\pi\:{is}\:{period}\right) \\ $$$$=−{sin}\left(\frac{\pi}{\mathrm{4}}\right)=−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$

Commented by kaivan.ahmadi last updated on 13/Nov/19

sin(21π+(π/4))=sin(π+(π/4))=−sin((π/4))=−((√2)/2)

$${sin}\left(\mathrm{21}\pi+\frac{\pi}{\mathrm{4}}\right)={sin}\left(\pi+\frac{\pi}{\mathrm{4}}\right)=−{sin}\left(\frac{\pi}{\mathrm{4}}\right)=−\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$

Commented by mathocean1 last updated on 14/Nov/19