Question Number 137813 by bramlexs22 last updated on 07/Apr/21
$$\mathrm{cos}\:\left(\mathrm{arctan}\:\left(\frac{\mathrm{21}}{\mathrm{60}}\right)\right)=? \\ $$
Answered by mr W last updated on 07/Apr/21
$${say}\:{t}=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{21}}{\mathrm{60}} \\ $$$$\mathrm{tan}\:{t}=\frac{\mathrm{21}}{\mathrm{60}}=\frac{\mathrm{7}}{\mathrm{20}} \\ $$$$\mathrm{cos}\:{t}=\frac{\mathrm{20}}{\:\sqrt{\mathrm{20}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} }}=\frac{\mathrm{20}}{\:\sqrt{\mathrm{449}}} \\ $$$${i}.{e}.\:\mathrm{cos}\:\left(\mathrm{arctan}\:\left(\frac{\mathrm{21}}{\mathrm{60}}\right)\right)=\frac{\mathrm{20}}{\:\sqrt{\mathrm{449}}} \\ $$
Commented by bramlexs22 last updated on 07/Apr/21
$${thank}\:{you} \\ $$