Question

If sin(x)=0.3090 , what is the approximate value of csc(x)?

Answer 1

$\sin x=0.3090\approx\dfrac13$

$\csc x=\dfrac1{\sin x}\implies\csc x\approx 3$

which makes 3.2362 likely the best choice.

Answer 2

Answer

3.2362

Explanation

To solve this, we are going to use the trig identity: $csc(x)=\frac{1}{sin(x)}$

We know that our problem that $sin(x)=0.3090$, so let's replace the value in our identity:

$csc(x)=\frac{1}{sin(x)}$

$csc(x)=\frac{1}{0.3090}$

$csc(x)=3.2362$

We can conclude that the approximate value of $csc(x)$ is 3.2362.