Find-sin-2-7-44-22-54-800-

Question Number 213693 by hardmath last updated on 13/Nov/24

$$\mathrm{Find}: \\ $$$$\mathrm{sin}^{\mathrm{2}} \:\left(\mathrm{7}°\:\mathrm{44}'\:\mathrm{22},\mathrm{54}''\right)\centerdot\mathrm{800} \\ $$

Commented by Ghisom last updated on 13/Nov/24

$$\mathrm{use}\:\mathrm{a}\:\mathrm{calculator} \\ $$$$\approx\mathrm{14}.\mathrm{5090174} \\ $$

Commented by hardmath last updated on 13/Nov/24

$$ \\ $$At least I need a solution to this, my dear friend

Commented by Frix last updated on 14/Nov/24

7°44′22.54′′=((1 393 127π)/(32 400 000)) What do you expect? There′s no “nice” result. 800sin^2 α =400(1−cos 2α)= =400(1−cos ((1 393 127π)/(16 200 000)))≈14.5090173571

$$\mathrm{7}°\mathrm{44}'\mathrm{22}.\mathrm{54}''=\frac{\mathrm{1}\:\mathrm{393}\:\mathrm{127}\pi}{\mathrm{32}\:\mathrm{400}\:\mathrm{000}} \\ $$$$\mathrm{What}\:\mathrm{do}\:\mathrm{you}\:\mathrm{expect}?\:\mathrm{There}'\mathrm{s}\:\mathrm{no}\:“\mathrm{nice}'' \\ $$$$\mathrm{result}. \\ $$$$\mathrm{800sin}^{\mathrm{2}} \:\alpha\:=\mathrm{400}\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}\alpha\right)= \\ $$$$=\mathrm{400}\left(\mathrm{1}−\mathrm{cos}\:\frac{\mathrm{1}\:\mathrm{393}\:\mathrm{127}\pi}{\mathrm{16}\:\mathrm{200}\:\mathrm{000}}\right)\approx\mathrm{14}.\mathrm{5090173571} \\ $$

Commented by mr W last updated on 14/Nov/24

$${a}\:{non}−{sense}\:{question}! \\ $$

Answered by mahdipoor last updated on 14/Nov/24

12 h = 360 degree ⇒ 1 h = 30 degree 60 min = 1h 60 sec = 1 min ⇒ 3600 sec = 1 h ⇒⇒ 7 h 44 min 22.45 sec = (7+((44)/(60))+((22.45)/(3600))) h = (7+((44)/(60))+((22.45)/(3600)))×((360)/(12)) degree = angle ....

$$\mathrm{12}\:{h}\:=\:\mathrm{360}\:{degree}\:\:\Rightarrow\:\mathrm{1}\:{h}\:=\:\mathrm{30}\:{degree} \\ $$$$\mathrm{60}\:{min}\:=\:\mathrm{1}{h}\: \\ $$$$\mathrm{60}\:{sec}\:=\:\mathrm{1}\:{min}\:\Rightarrow\:\mathrm{3600}\:{sec}\:=\:\mathrm{1}\:{h} \\ $$$$\Rightarrow\Rightarrow\:\mathrm{7}\:{h}\:\:\:\mathrm{44}\:{min}\:\:\:\mathrm{22}.\mathrm{45}\:{sec}\:= \\ $$$$\left(\mathrm{7}+\frac{\mathrm{44}}{\mathrm{60}}+\frac{\mathrm{22}.\mathrm{45}}{\mathrm{3600}}\right)\:{h}\:=\: \\ $$$$\left(\mathrm{7}+\frac{\mathrm{44}}{\mathrm{60}}+\frac{\mathrm{22}.\mathrm{45}}{\mathrm{3600}}\right)×\frac{\mathrm{360}}{\mathrm{12}}\:{degree}\:=\:{angle} \\ $$$$…. \\ $$

Answered by MathematicalUser2357 last updated on 14/Nov/24

sin^2 (7°44′22.54′′)∙800 =[sin{(7+((44)/(60))+((22.54)/(60×60)))°}]^2 ∙800 So... (sin((7+((44)/(60))+((22.54)/(60×60)))°))^2 ×800 14.509017

$$\mathrm{sin}^{\mathrm{2}} \left(\mathrm{7}°\mathrm{44}'\mathrm{22}.\mathrm{54}''\right)\centerdot\mathrm{800} \\ $$$$=\left[\mathrm{sin}\left\{\left(\mathrm{7}+\frac{\mathrm{44}}{\mathrm{60}}+\frac{\mathrm{22}.\mathrm{54}}{\mathrm{60}×\mathrm{60}}\right)°\right\}\right]^{\mathrm{2}} \centerdot\mathrm{800} \\ $$$$\mathrm{So}… \\ $$$$\left(\mathrm{sin}\left(\left(\mathrm{7}+\frac{\mathrm{44}}{\mathrm{60}}+\frac{\mathrm{22}.\mathrm{54}}{\mathrm{60}×\mathrm{60}}\right)°\right)\right)^{\mathrm{2}} ×\mathrm{800} \\ $$$$\mathrm{14}.\mathrm{509017} \\ $$

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