Question

if \\(sin \theta \approx 0.3090\\), what is the approximate value of \\(csc \theta\\)?
\\(\bigcirc\\) 0.5559
\\(\bigcirc\\) 1.3090
\\(\bigcirc\\) 3.2362
\\(\bigcirc\\) 10.4733

Explanation:

Step1: Recall the reciprocal identity of sine and cosecant

The cosecant of an angle \(\theta\) is the reciprocal of the sine of \(\theta\), that is \(\csc\theta=\frac{1}{\sin\theta}\) (for \(\sin\theta
eq0\)).

Step2: Substitute the given value of \(\sin\theta\)

We are given that \(\sin\theta\approx0.3090\). So we substitute this value into the formula for \(\csc\theta\): \(\csc\theta\approx\frac{1}{0.3090}\).

Step3: Calculate the value

Calculating \(\frac{1}{0.3090}\approx3.2362\).

Answer:

3.2362 (the option with 3.2362)