Question

topic: identifying the six trigonometric functions
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on you
what is the value of \\(\csc 47^\circ\\) to the nearest thousandth?
\\(\csc 47^\circ \approx\\)
the solution is \\(\boxed{}\\)

Explanation:

Step1: Recall the reciprocal identity of cosecant

The cosecant function is the reciprocal of the sine function, so $\csc\theta=\frac{1}{\sin\theta}$. For $\theta = 47^\circ$, we have $\csc47^\circ=\frac{1}{\sin47^\circ}$.

Step2: Calculate $\sin47^\circ$

Using a calculator (in degree mode), we find that $\sin47^\circ\approx0.7313537016$.

Step3: Calculate the reciprocal

Now, we take the reciprocal of $\sin47^\circ$: $\frac{1}{0.7313537016}\approx1.367$.

Answer:

1.367