Cosec pi

The value of cosec pi is not defined. Cosec pi radians in degrees is written as csc ((π) × 180°/π), i.e., cosec (180°). In this article, we will discuss the methods to find the value of cosec pi with examples.

• Cosec pi: not defined
• Cosec (-pi): not defined
• Cosec pi in degrees: csc (180°)

What is the Value of Cosec pi?

The value of csc pi is not defined. Cosec pi can also be expressed using the equivalent of the given angle (pi) in degrees (180°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi radians = pi × (180°/pi) = 180° or 180 degrees
∴ csc pi = cosec π = cosec(180°) = not defined

Explanation:

For csc pi, the angle pi lies on the negative x-axis. Thus, cosec pi value = not defined
Since the cosecant function is a periodic function, we can represent csc pi as, cosec pi = cosec(pi + n × 2pi), n ∈ Z.
⇒ csc pi = csc 3pi = cosec 5pi , and so on.
Note: Since, cosecant is an odd function, the value of cosec(-pi) = -cosec(pi) = not defined.

Methods to Find Value of Cosec pi

The value of csc pi is given as not defined. We can find the value of csc pi by:

• Using Trigonometric Functions
• Using Unit Circle

Cosec pi in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cosec pi as:

• ± 1/√(1-cos²(pi))
• ± √(1 + tan²(pi))/tan(pi)
• ± √(1 + cot²(pi))
• ± sec(pi)/√(sec²(pi) - 1))
• 1/sin(pi)

Note: Since pi lies on the negative x-axis, the final value of cosec pi is not defined.

We can use trigonometric identities to represent cosec pi as,

• csc(pi - pi) = cosec 0
• -cosec(pi + pi) = -cosec 2pi
• sec(pi/2 - pi) = sec(-pi/2)
• -sec(pi/2 + pi) = -sec 3pi/2

Cosec pi Using Unit Circle

To find the value of csc π using the unit circle:

• Rotate ‘r’ anticlockwise to form pi angle with the positive x-axis.
• The cosec of pi equals the reciprocal of the y-coordinate(0) of the point of intersection (-1, 0) of unit circle and r.

Hence the value of csc pi = 1/y = not defined 

☛ Also Check:

• sin 11pi/6
• cos 7pi/3
• csc pi/4
• sin 5pi/12
• cos pi/3
• tan 13pi/12

FAQs on Cosec pi

What is Cosec pi?

Cosec pi is the value of cosecant trigonometric function for an angle equal to π. The value of cosec pi is not defined.

What is the Value of Cosec pi in Terms of Sec pi?

Since the cosec function can be represented using the secant function, we can write cosec pi as -sec(pi)/√(sec²(pi) - 1). The value of sec pi is equal to -1.

How to Find Cosec pi in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of csc pi can be given in terms of other trigonometric functions as:

• ± 1/√(1-cos²(pi))
• ± √(1 + tan²(pi))/tan(pi)
• ± √(1 + cot²(pi))
• ± sec(pi)/√(sec²(pi) - 1))
• 1/sin(pi)

☛ Also check: trigonometry table

What is the Value of Cosec pi in Terms of Cot pi?

We can represent the cosec function in terms of the cotangent function using trig identities, cosec pi can be written as √(1 + cot²(pi)). 

How to Find the Value of Cosec pi?

The value of csc pi can be calculated by constructing an angle of π radians with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of cosec pi is equal to the reciprocal of the y-coordinate (0). ∴ csc pi = not defined.