Cosec 90 Degrees

The value of cosec 90 degrees is 1. Cosec 90 degrees in radians is written as cosec (90° × π/180°), i.e., cosec (π/2) or cosec (1.570796. . .). In this article, we will discuss the methods to find the value of cosec 90 degrees with examples.

• Cosec 90°: 1
• Cosec (-90 degrees): -1
• Cosec 90° in radians: cosec (π/2) or cosec (1.5707963 . . .)

What is the Value of Cosec 90 Degrees?

The value of cosec 90 degrees is 1. Cosec 90 degrees can also be expressed using the equivalent of the given angle (90 degrees) in radians (1.57079 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 90 degrees = 90° × (π/180°) rad = π/2 or 1.5707 . . .
∴ cosec 90° = cosec(1.5707) = 1

Explanation:

For cosec 90 degrees, the angle 90° lies on the positive y-axis. Thus cosec 90° value = 1
Since the cosecant function is a periodic function, we can represent cosec 90° as, cosec 90 degrees = cosec(90° + n × 360°), n ∈ Z.
⇒ cosec 90° = cosec 450° = cosec 810°, and so on.
Note: Since, cosecant is an odd function, the value of cosec(-90°) = -cosec(90°).

Methods to Find Value of Cosec 90 Degrees

The value of cosec 90° is given as 1. We can find the value of cosec 90 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cosec 90 Degrees Using Unit Circle

To find the value of cosec 90 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 90° angle with the positive x-axis.
• The cosec of 90 degrees equals the reciprocal of the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

Hence the value of cosec 90° = 1/y = 1

Cosec 90° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cosec 90 degrees as:

• ± 1/√(1-cos²(90°))
• ± √(1 + tan²(90°))/tan 90°
• ± √(1 + cot²(90°))
• ± sec 90°/√(sec²(90°) - 1)
• 1/sin 90°

We can use trigonometric identities to represent cosec 90° as,

• cosec(180° - 90°) = cosec 90°
• -cosec(180° + 90°) = -cosec 270°
• sec(90° - 90°) = sec 0°
• -sec(90° + 90°) = -sec 180°

Note: Since 90° lies on the positive y-axis, the final value of cosec 90° will be positive.

☛ Also Check:

• cosec 60 degrees
• cosec 20 degrees
• cosec 45 degrees
• cosec 1200 degrees
• cosec 0 degrees
• cosec 30 degrees

FAQs on Cosec 90 Degrees

What is Cosec 90 Degrees?

Cosec 90 degrees is the value of cosecant trigonometric function for an angle equal to 90 degrees. The value of cosec 90° is 1.

How to Find the Value of Cosec 90 Degrees?

The value of cosec 90 degrees can be calculated by constructing an angle of 90° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cosec 90° is equal to the reciprocal of the y-coordinate (1). ∴ cosec 90° = 1.

How to Find Cosec 90° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cosec 90° can be given in terms of other trigonometric functions as:

• ± 1/√(1-cos²(90°))
• ± √(1 + tan²(90°))/tan 90°
• ± √(1 + cot²(90°))
• ± sec 90°/√(sec²(90°) - 1)
• 1/sin 90°

☛ Also check: trigonometry table

What is the Value of Cosec 90 Degrees in Terms of Cot 90°?

We can represent the cosec function in terms of the cotangent function using trig identities, cosec 90° can be written as √(1 + cot²(90°)). Here, the value of cot 90° is equal to 0.

What is the Exact Value of Cosec 90 Degrees?

The exact value of cosec 90 degrees is 1.