Answer

Verified

339.3k+ views

**Hint:**In this question, we have to find the value of the cosecant of 180 degrees, cosecant is a trigonometric function. So to solve the question, we must know the details of trigonometric functions and how to find their values. The trigonometry helps us to find the relation between the sides of a right-angled triangle that is the base, the perpendicular and the hypotenuse. The trigonometric functions have different signs in different quadrants, so by using the above information, we can find out the cosecant of the given angle.

**Complete step by step solution:**

We know that –

$

\csc x = \dfrac{1}{{\sin x}} \\

\Rightarrow \csc 180 = \dfrac{1}{{\sin 180}} \\

$

Now,

$\sin (180^\circ ) = \sin (180^\circ + 0^\circ )$

We know that sine is negative in the third quadrant, so –

$

\sin (180^\circ ) = - \sin (0^\circ ) \\

\Rightarrow \sin (180^\circ ) = 0^\circ \\

\Rightarrow \csc 180 = \dfrac{1}{0} = \infty \\

$

Hence, the value of $\csc (180^\circ )$ is not defined.

**Note:**Sine, cosine and tangent are the main functions of the trigonometry while cosecant, secant and cotangent functions are their reciprocals respectively. All the trigonometric functions have a positive value in the first quadrant. In the second quadrant, sine is positive while all the other functions are negative; in the third quadrant, tan function is positive while all other functions are positive; and in the fourth quadrant, cosine function is positive while all others are negative, that’s why $\sin (180 + \theta ) = - \sin \theta $ . We also know that the trigonometric functions are periodic, we know the value of the cosecant function when the angle lies between 0 and $\dfrac{\pi }{2}$ . That’s why we use the periodic property of these functions to find the value of the cosecant of the angles greater than $\dfrac{\pi }{2}$ .

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

What happens when entropy reaches maximum class 11 chemistry JEE_Main

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Explain why a There is no atmosphere on the moon b class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

Can anyone list 10 advantages and disadvantages of friction

State and prove Bernoullis theorem class 11 physics CBSE

The ice floats on water because A solid have lesser class 9 chemistry CBSE

State Newtons formula for the velocity of sound in class 11 physics CBSE