Question

How do you find the value of $\csc 63$?

Answer 1

Here in this question we have been asked to find the value of $\csc 63$ . From the basic concepts of trigonometry we know that the value of $\csc$ is the reciprocal of $\sin$ which is mathematically given as $\dfrac{1}{\sin }$ .

Complete step-by-step solution:
Now considering from the question we have been asked to find the value of $\csc 63$ .
From the basic concepts of trigonometry we know that the value of $\csc$ is the reciprocal of $\sin$ which is mathematically given as $\dfrac{1}{\sin }$ .
From the basic concepts of trigonometry we also know that the value of $\sin {{60}^{\circ }}$ is given as $\dfrac{\sqrt{3}}{2}=0.866$ and the range of the sine is from zero to one. Hence the value of sine of 63 will be greater than 0.866 and near to it and less than one.
If we use the calculator and calculate its value then we will have $0.89$ .
Similarly we know that the value of $\csc {{60}^{\circ }}$ is $\dfrac{2}{\sqrt{3}}=1.154$ .
Therefore the required value will be $\csc 63=\dfrac{1}{\sin 63}\Rightarrow \dfrac{1}{0.89}=1.12$.

Note: While answering questions of this type we should be sure with the concepts that we are going to apply and the calculations that we are going to perform in between. This is a very short and simple question. Similarly we can find the value of any other trigonometric function. For example if we consider cosine function then we will use the formula given as $\cos \theta =\sqrt{1-{{\sin }^{2}}\theta }$ and we will have the result as $\cos 63=\sqrt{1-{{\left( 0.89 \right)}^{2}}}=0.456$ .