Mathematics: What co secant 0 if tan 0 =3/4

What co secant 0 if tan 0 =3/4 - id00343052079, perezrhonda30

Ответ:

annekacoleman

06.01.2022

$\tan\theta=\dfrac340$

$\cot\theta=\dfrac1{\tan\theta}=\dfrac430$

$\csc^2\theta=1+\cot^2\theta$
$\csc\theta=\pm\sqrt{1+\left(\dfrac43\right)^2}=\pm\dfrac53$

Without any more information, it's impossible to tell whether the cosecant is positive or negative. For example, if $\theta=\tan^{-1}\dfrac34$ , then

$\tan\left(\tan^{-1}\dfrac34\right)=\dfrac34$
$\tan\left(\pi+\tan^{-1}\dfrac34\right)=\dfrac34$

but

$\csc\left(\tan^{-1}\dfrac34\right)=\dfrac53$
$\csc\left(\pi+\tan^{-1}\dfrac34\right)=-\dfrac53$