Question

How do you find the value of \[{\rm{cosec}}90^\circ \]?

Answer 1

Hint: Here, we have to find the Trigonometric Value of the given Trigonometric Ratio. We will find the Trigonometric Ratio in terms of the sine function. Then by using the Trigonometric Value of the sine function of the obtained angle, we will find the required answer. Trigonometric Ratios of a Particular angle are the ratios of the sides of a right-angled triangle with respect to any of its acute angle.

Formula Used:
We will use the following formula:
1) Trigonometric Co-ratio \[\cos {\rm{ec}}x = \dfrac{1}{{\sin x}}\]
2) Trigonometric Value of \[\sin 90^\circ = 1\]

Complete step by step solution:
We are given a Trigonometric Ratio \[{\rm{cosec}}90^\circ \].
We know that the Trigonometric Co-ratio of \[\cos {\rm{ec}}x\] is \[\dfrac{1}{{\sin x}}\] i.e., \[\cos {\rm{ec}}x = \dfrac{1}{{\sin x}}\].
Now, we will find the value of \[{\rm{cosec}}90^\circ \] by using the Trigonometric Co-ratio, so we get
\[ \Rightarrow \cos {\rm{ec90}}^\circ = \dfrac{1}{{\sin 90^\circ }}\]
We know that the Trigonometric Value of \[\sin 90^\circ = 1\].
By substituting the Trigonometric Value, we get
\[ \Rightarrow \cos {\rm{ec90}}^\circ = \dfrac{1}{1}\]
\[ \Rightarrow \cos {\rm{ec90}}^\circ = 1\]

Therefore, the Trigonometric Value of \[{\rm{cosec}}90^\circ \] is 1.

Note:
We know that Trigonometric Equation is defined as an equation involving trigonometric ratios. Trigonometric identity is an equation that is always true for all the variables. We should know that we have many trigonometric identities that are related to all the other trigonometric equations. We should remember that the trigonometric ratio and the co-trigonometric ratio is always reciprocal to each other. Trigonometric Ratios are used to find the relationships between the sides of a right-angle triangle. We should remember that all the trigonometric ratios can be written in the form of a basic Trigonometric Ratio of sine and cosine.