Find the value of the expression.Round your result to two decimal places. $$\operatorname { arccsc } ( - 24 )$$
A)1.61
B)1.53
C)0.04
D)0.96
E)-0.04

Question

Find the value of the expression.Round your result to two decimal places.​ $$\operatorname { arccsc } ( - 24 )$$ ​
A)1.61
B)1.53
C)0.04
D)0.96
E)-0.04

Quizplus · Accepted Answer

The arccsc function is the inverse of the cosecant function, which means $\operatorname{arccsc}(x) = \theta$ implies $\csc(\theta) = x$. Given $\operatorname{arccsc}(-24)$, we're looking for an angle $\theta$ whose cosecant is -24. Since $\csc(\theta) = \frac{1}{\sin(\theta)}$, we have $\sin(\theta) = \frac{1}{-24}$. Using the definition of arcsin, we find $\theta = \arcsin\left(\frac{1}{-24}\right)$. Calculating this gives $\theta \approx -0.0416$ radians, which rounds to -0.04.

Find the Value of the Expression arccsc⁡(−24)\operatorname { arccsc } ( - 24 )arccsc(−24)

Find the Value of the Expression $\operatorname { arccsc } ( - 24 )$