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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) = ?

Verified Answer :

bartdrinksmalk

In quadrant IV, we have
\(\csc\theta<0\)
and
\(\cot\theta<0\)

We can use the identity
\(\csc^{2} \theta=1+\cot^{2} \theta\)
\(\csc\theta=\pm\sqrt{1+\cot^{2} \theta}\)
Since \(\csc\theta<0\), we get
\(\csc\theta=-\sqrt{1+\cot^{2} \theta}\)

obasola1

Answer:

cosecα=\(-\sqrt{1+cot^{2}\alpha }\)

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

\(cosec^{2} \alpha =1+cot^{2}\alpha \\cosec\alpha ==+/-\sqrt{1+cot^{2}\alpha }\)

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

cosecα=\(-\sqrt{1+cot^{2}\alpha }\)

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

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