Respuesta :

LammettHash
[tex]\tan\theta=\dfrac34>0[/tex]

[tex]\cot\theta=\dfrac1{\tan\theta}=\dfrac43>0[/tex]

[tex]\csc^2\theta=1+\cot^2\theta[/tex]
[tex]\csc\theta=\pm\sqrt{1+\left(\dfrac43\right)^2}=\pm\dfrac53[/tex]

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

[tex]\tan\left(\tan^{-1}\dfrac34\right)=\dfrac34[/tex]
[tex]\tan\left(\pi+\tan^{-1}\dfrac34\right)=\dfrac34[/tex]

but

[tex]\csc\left(\tan^{-1}\dfrac34\right)=\dfrac53[/tex]
[tex]\csc\left(\pi+\tan^{-1}\dfrac34\right)=-\dfrac53[/tex]

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