Question

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

Answer 1

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

Answer 2

In quadrant IV, we have
$\csc\theta$
and
$\cot\theta$

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