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Question Number 195229 by mathlove last updated on 28/Jul/23

below equestion is show elips and hypharabollah (x^2 /(cos3))+(y^2 /(sin3))=1

$${below}\:{equestion}\:{is}\:{show}\:\:{elips}\:{and} \\ $$$${hypharabollah} \\ $$$$\frac{{x}^{\mathrm{2}} }{{cos}\mathrm{3}}+\frac{{y}^{\mathrm{2}} }{{sin}\mathrm{3}}=\mathrm{1} \\ $$

Commented by mr W last updated on 28/Jul/23

(π/2)<3<π ⇒cos 3 <0

$$\frac{\pi}{\mathrm{2}}<\mathrm{3}<\pi \\ $$$$\Rightarrow\mathrm{cos}\:\mathrm{3}\:<\mathrm{0} \\ $$

Commented by mathlove last updated on 28/Jul/23

way cos3<^? 0

$${way} \\ $$$${cos}\mathrm{3}\overset{?} {<}\mathrm{0} \\ $$

Commented by mathlove last updated on 28/Jul/23

i understand 3 is no degree but 3 is radian

$${i}\:{understand}\:\mathrm{3}\:{is}\:{no}\:{degree} \\ $$$${but}\:\mathrm{3}\:{is}\:{radian} \\ $$

Commented by BaliramKumar last updated on 28/Jul/23

(x^2 /(cos3)) + (y^2 /(sin3)) = 1 (x^2 /(−0.98999)) + (y^2 /(0.14112)) = 1 (y^2 /(0.14112)) − (x^2 /(0.98999)) = 1 b^2 = 0.14112, a^2 = 0.98999 b = ±(√(0.14112)) , a = ±(√(0.98999)) (y^2 /((±(√(0.14112)))^2 )) − (x^2 /((±(√(0.98999)))^2 )) = 1 (y^2 /((b)^2 )) − (x^2 /((a)^2 )) = 1 hyperbolla

$$ \\ $$$$\frac{{x}^{\mathrm{2}} }{{cos}\mathrm{3}}\:+\:\frac{{y}^{\mathrm{2}} }{{sin}\mathrm{3}}\:=\:\mathrm{1} \\ $$$$\frac{{x}^{\mathrm{2}} }{−\mathrm{0}.\mathrm{98999}}\:+\:\frac{{y}^{\mathrm{2}} }{\mathrm{0}.\mathrm{14112}}\:=\:\mathrm{1} \\ $$$$\:\frac{{y}^{\mathrm{2}} }{\mathrm{0}.\mathrm{14112}}\:−\:\frac{{x}^{\mathrm{2}} }{\mathrm{0}.\mathrm{98999}}\:=\:\mathrm{1} \\ $$$${b}^{\mathrm{2}} \:=\:\mathrm{0}.\mathrm{14112},\:\:\:\:\:\:\:{a}^{\mathrm{2}} \:=\:\mathrm{0}.\mathrm{98999} \\ $$$${b}\:=\:\pm\sqrt{\mathrm{0}.\mathrm{14112}}\:\:\:,\:\:\:\:\:\:\:{a}\:=\:\pm\sqrt{\mathrm{0}.\mathrm{98999}} \\ $$$$ \\ $$$$\:\frac{{y}^{\mathrm{2}} }{\left(\pm\sqrt{\mathrm{0}.\mathrm{14112}}\right)^{\mathrm{2}} }\:−\:\frac{{x}^{\mathrm{2}} }{\left(\pm\sqrt{\mathrm{0}.\mathrm{98999}}\right)^{\mathrm{2}} }\:=\:\mathrm{1} \\ $$$$\:\frac{{y}^{\mathrm{2}} }{\left({b}\right)^{\mathrm{2}} }\:−\:\frac{{x}^{\mathrm{2}} }{\left({a}\right)^{\mathrm{2}} }\:=\:\mathrm{1} \\ $$$${hyperbolla} \\ $$

Commented by mr W last updated on 28/Jul/23

why does it make no real number? cos 3=−a^2 or a=(√(−cos 3))

$${why}\:{does}\:{it}\:{make}\:{no}\:{real}\:{number}? \\ $$$$\mathrm{cos}\:\mathrm{3}=−{a}^{\mathrm{2}} \:{or}\:{a}=\sqrt{−\mathrm{cos}\:\mathrm{3}} \\ $$

Commented by mr W last updated on 28/Jul/23

you musn′t take a^2 =cos 3. why not take a^2 =−cos 3?

$${you}\:{musn}'{t}\:{take}\:{a}^{\mathrm{2}} =\mathrm{cos}\:\mathrm{3}.\:{why}\:{not} \\ $$$${take}\:{a}^{\mathrm{2}} =−\mathrm{cos}\:\mathrm{3}? \\ $$

Commented by mr W last updated on 28/Jul/23

Commented by mr W last updated on 30/Jul/23

when normal earth people write sin 3 or cos 3, they mean 3 rad, not 3 degrees. if they want to mean 3 degrees, they explictly write sin 3° or cos 3°. this is a common convention, which normal earth people follow:

$${when}\:{normal}\:{earth}\:{people}\:{write}\: \\ $$$${sin}\:\mathrm{3}\:{or}\:\mathrm{cos}\:\mathrm{3},\:{they}\:{mean}\:\mathrm{3}\:{rad},\:{not} \\ $$$$\mathrm{3}\:{degrees}.\:{if}\:{they}\:{want}\:{to}\:{mean}\:\mathrm{3} \\ $$$${degrees},\:{they}\:{explictly}\:{write}\:\:\mathrm{sin}\:\mathrm{3}°\:{or} \\ $$$$\mathrm{cos}\:\mathrm{3}°.\:{this}\:{is}\:{a}\:{common}\:{convention}, \\ $$$${which}\:{normal}\:{earth}\:{people}\:{follow}: \\ $$

Commented by mr W last updated on 30/Jul/23

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