Question

What does \[csc\ 0\] equal ?

Answer 1

Hint: In this question, we need to find the value of \[cosec\ 0^{o}\] . We can find the value of \[cosec\ 0^{o}\] by using trigonometric identities and ratios. The cosecant is nothing but a ratio of the hypotenuse of a right angle to the opposite side of the right angle. The basic trigonometric functions are sine, cosine and tangent. The values \[\sin 0^{o}\] are used to find the value. With the help of the Trigonometric functions , we can find the value of \[cosec\ 0^{o}\] .
Formula used :
\[cosec\ \theta = \dfrac{1}{\sin \theta }\]
Trigonometry table :

Angle	\[0^{o}\]	\[30^{o}\]	\[45^{o}\]	\[60^{o}\]	\[90^{o}\]
sine	\[0\]	\[\dfrac{{1}}{2}\]	\[\dfrac{1}{\sqrt{2}}\]	\[\dfrac{\sqrt{3}}{2}\]	\[1\]

Complete step by step solution:
We can find the value of \[cosec\ 0^{o}\] by using the cosine function.
We know that
\[cosec\ \theta = \dfrac{1}{\sin \theta}\]
Here \[\theta = 0^{o}\]
Thus we get,
\[cosec\ 0^{o} = \dfrac{1}{\sin 0^{o}}\]
From the trigonometric table, the value of \[\sin 0^{o}\] is \[0\]
By substituting the known values,
We get ,
\[cosec\ 0^{o} = \dfrac{1}{0}\]
By dividing,
We get ,
\[cosec\ 0^{o} = \infty\]
Thus we get the value of \[cosec\ 0^{o}\] is equal to \[\infty\] which is infinite or not defined.
Final answer :
Since the value of \[cosec 0^{o}\] is infinite, therefore the value of \[cosec 0^{o}\] is not defined .

Note: The concept used in this problem is trigonometric identities and ratios. Trigonometric identities are nothing but they involve trigonometric functions including variables and constants. The common technique used in this problem is the use of trigonometric functions. Geometrically, \[cosec\ 0^{o}\] lies in the first quadrant. We need to note that \[\dfrac{0}{1}\] is \[0\] and \[\dfrac{1}{0}\] is \[\infty\] .