Answer
385.8k+ views
Hint:In this question, we have to find the value of all the trigonometric functions which are sine, cosine, tangent, cotangent, cosecant and secant for the $\dfrac{{5\pi }}{2}$. Firstly, know that the $\dfrac{{5\pi }}{2} = 2\pi + \dfrac{\pi }{2}$ . Now, $2\pi $is the angle where the trigonometric functions do not change. And, hence finding the values.
Complete step by step answer:
In this respective question, firstly we are splitting the angle given into those values whose values are learned by everybody which are in the form of $\pi ,2\pi \ldots $ and so on.So, writing $\dfrac{{5\pi }}{2}$ as $2\pi + \dfrac{\pi }{2}$. Make sure that the quadrant now exists to be first where all trigonometric functions are positive. And also, at $\pi ,2\pi \ldots $ the trigonometric functions do not change. Trigonometric functions would change at $\dfrac{{3\pi }}{2},\dfrac{{5\pi }}{2} \ldots $
The functions change as an example: $\sin \to \cos $,$\cos ec \to \sec ,\tan \to \cot $ and vice-versa.Finding the values
$\sin \left( {2\pi + \dfrac{\pi }{2}} \right) = \sin \left( {\dfrac{\pi }{2}} \right) = 1$
$\Rightarrow\cos \left( {2\pi + \dfrac{\pi }{2}} \right) = \cos \left( {\dfrac{\pi }{2}} \right) = 0$
$
\Rightarrow\tan \left( {2\pi + \dfrac{\pi }{2}} \right) = \tan \left( {\dfrac{\pi }{2}} \right) = \infty \\
\Rightarrow\cot \left( {2\pi + \dfrac{\pi }{2}} \right) = \cot \left( {\dfrac{\pi }{2}} \right) = 0 \\
\Rightarrow\cos ec\left( {2\pi + \dfrac{\pi }{2}} \right) = \cos ec\left( {\dfrac{\pi }{2}} \right) = 1 \\
\therefore\sec \left( {2\pi + \dfrac{\pi }{2}} \right) = \sec \left( {\dfrac{\pi }{2}} \right) = \infty \\
$
These are the values for the given angle for all the trigonometric functions.
Note:Make sure you have learnt the full trigonometric table. The quadrants should be observed carefully. Learn which functions are positive in which quadrant. In the first quadrant, all functions are positive. In the second, sine and cosecant are positive, else negative. In the third quadrant, tangent and cotangent are positive. In fourth, cosecant and secant are positive.
Complete step by step answer:
In this respective question, firstly we are splitting the angle given into those values whose values are learned by everybody which are in the form of $\pi ,2\pi \ldots $ and so on.So, writing $\dfrac{{5\pi }}{2}$ as $2\pi + \dfrac{\pi }{2}$. Make sure that the quadrant now exists to be first where all trigonometric functions are positive. And also, at $\pi ,2\pi \ldots $ the trigonometric functions do not change. Trigonometric functions would change at $\dfrac{{3\pi }}{2},\dfrac{{5\pi }}{2} \ldots $
The functions change as an example: $\sin \to \cos $,$\cos ec \to \sec ,\tan \to \cot $ and vice-versa.Finding the values
$\sin \left( {2\pi + \dfrac{\pi }{2}} \right) = \sin \left( {\dfrac{\pi }{2}} \right) = 1$
$\Rightarrow\cos \left( {2\pi + \dfrac{\pi }{2}} \right) = \cos \left( {\dfrac{\pi }{2}} \right) = 0$
$
\Rightarrow\tan \left( {2\pi + \dfrac{\pi }{2}} \right) = \tan \left( {\dfrac{\pi }{2}} \right) = \infty \\
\Rightarrow\cot \left( {2\pi + \dfrac{\pi }{2}} \right) = \cot \left( {\dfrac{\pi }{2}} \right) = 0 \\
\Rightarrow\cos ec\left( {2\pi + \dfrac{\pi }{2}} \right) = \cos ec\left( {\dfrac{\pi }{2}} \right) = 1 \\
\therefore\sec \left( {2\pi + \dfrac{\pi }{2}} \right) = \sec \left( {\dfrac{\pi }{2}} \right) = \infty \\
$
These are the values for the given angle for all the trigonometric functions.
Note:Make sure you have learnt the full trigonometric table. The quadrants should be observed carefully. Learn which functions are positive in which quadrant. In the first quadrant, all functions are positive. In the second, sine and cosecant are positive, else negative. In the third quadrant, tangent and cotangent are positive. In fourth, cosecant and secant are positive.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)