Yenix23
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Write the first trigonometric function in terms of the second for theta in the given quadrant:
csc(theta), cot(theta); theta in quadrant IV
csc(theta) = ?

Respuesta :

bartdrinksmalk
In quadrant IV, we have
[tex]\csc\theta<0[/tex]
and
[tex]\cot\theta<0[/tex]

We can use the identity
[tex]\csc^{2} \theta=1+\cot^{2} \theta[/tex]
[tex]\csc\theta=\pm\sqrt{1+\cot^{2} \theta}[/tex]
Since [tex]\csc\theta<0[/tex], we get
[tex]\csc\theta=-\sqrt{1+\cot^{2} \theta}[/tex]
obasola1

Answer:

cosecα=[tex]-\sqrt{1+cot^{2}\alpha }[/tex]

Step-by-step explanation:

Write the first trigonometric function in terms of the second for theta in the given quadrant:

csc(theta), cot(theta); theta in quadrant IV

csc(theta) = ?

from trigonometric identity , we know that

[tex]cosec^{2} \alpha =1+cot^{2}\alpha \\cosec\alpha ==+/-\sqrt{1+cot^{2}\alpha }[/tex]

since cosecα is negative in the fourth quadrant , we can solve it as thus

cosecα=[tex]-\sqrt{1+cot^{2}\alpha }[/tex]

i have only used alpha in place of theta, aside from that ,the answer is thus the above

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