Question

Find the value of $\cos ec\,0$.

Answer 1

Hint: As we know that the above question is related to trigonometry as cosecant is the trigonometric ratio. The short form is cosec. It is the reciprocal value of sine. It can be written as $\cos ec = \dfrac{1}{{\sin }}$. Cosecant is defined as the ratio of the hypotenuse in a right-angled triangle to the side opposite of an acute triangle. In this question, we will convert cosec in terms of sine and then we solve it.

Complete step-by-step solution:
We have to find the value of $\cos ec\,0$. It is the reciprocal of sin.
Let us assume we have to find the value of $\cos ec\,x$.
We can write it terms of sine: $\cos ec\,x = \dfrac{1}{{\sin x}}$.
Here we have $x = 0$.
Therefore by putting this in the expression we have $\cos ec\,0 = \dfrac{1}{{\sin 0}}$.
We know that the value of $\sin 0$ is $0$. So it gives us the value $\cos ec\,0 = \dfrac{1}{0}$.
Now we know that there is no such defined value of $\dfrac{1}{0}$.
So it gives us the value: $\cos ec\,0 = $undefined.

Hence the required value of $\cos ec\,0$ is undefined.

Note: Before solving this kind of question we should be fully aware of the trigonometric ratios and their relations. The value of $\cos ec\,\theta $in term of hypotenuse and perpendicular is $\cos ec\,\theta = \dfrac{h}{p}$, where $h$ is the hypotenuse and $p$is the perpendicular. It can also be derived from the sine formula as $\sin \theta = \dfrac{p}{h}$, so cosec is reciprocal of sin i.e. $\cos ec\theta = \dfrac{1}{{\dfrac{p}{h}}} \Rightarrow \dfrac{h}{p}$.