If $\theta$ is an angle such that $\sin \left(\theta \right)=0.3030$, what is the approximate value of $\csc \left(\theta \right)$?

• A. $1.3090$
• B. $0.5559$
• C. $10.4733$
• D. $3.2362$

Answer: (D)

Verified step by step guidance

1. Recall the definition of the cosecant function: \(\csc(\theta) = \frac{1}{\sin(\theta)}\).
2. Given that \(\sin(\theta) = 0.3030\), substitute this value into the cosecant formula to get \(\csc(\theta) = \frac{1}{0.3030}\).
3. Set up the division to find the reciprocal of 0.3030, which will give the value of \(\csc(\theta)\).
4. Perform the division carefully to approximate the value of \(\csc(\theta)\) without rounding prematurely.
5. Interpret the result as the approximate value of \(\csc(\theta)\) corresponding to the given sine value.