Cot 90 Degrees

The value of cot 90 degrees is 0. Cot 90 degrees in radians is written as cot (90° × π/180°), i.e., cot (π/2) or cot (1.570796. . .). In this article, we will discuss the methods to find the value of cot 90 degrees with examples.

• Cot 90°: 0
• Cot (-90 degrees): 0
• Cot 90° in radians: cot (π/2) or cot (1.5707963 . . .)

What is the Value of Cot 90 Degrees?

The value of cot 90 degrees is 0. Cot 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 . . .
∴ cot 90° = cot(1.5707) = 0

Explanation:

For cot 90 degrees, the angle 90° lies on the positive y-axis. Thus, cot 90° value = 0
Since the cotangent function is a periodic function, we can represent cot 90° as, cot 90 degrees = cot(90° + n × 180°), n ∈ Z.
⇒ cot 90° = cot 270° = cot 450°, and so on.
Note: Since, cotangent is an odd function, the value of cot(-90°) = -cot(90°) = 0.

Methods to Find Value of Cot 90 Degrees

The value of cot 90° is given as 0. We can find the value of cot 90 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cot 90° in Terms of Trigonometric Functions

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

• cos(90°)/sin(90°)
• ± cos 90°/√(1 - cos²(90°))
• ± √(1 - sin²(90°))/sin 90°
• ± 1/√(sec²(90°) - 1)
• ± √(cosec²(90°) - 1)
• 1/tan 90°

Note: Since 90° lies on the positive y-axis, the final value of cot 90° is 0.

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

• tan (90° - 90°) = tan 0°
• -tan (90° + 90°) = -tan 180°
• -cot (180° - 90°) = -cot 90°

Cot 90 Degrees Using Unit Circle

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

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

Hence the value of cot 90° = x/y = 0

☛ Also Check:

• cot 600 degrees
• cot 238 degrees
• cot 11 degrees
• cot 240 degrees
• cot 132 degrees
• cot 13 degrees

FAQs on Cot 90 Degrees

What is Cot 90 Degrees?

Cot 90 degrees is the value of cotangent trigonometric function for an angle equal to 90 degrees. The value of cot 90° is 0.

What is the Value of Cot 90° in Terms of Sec 90°?

We can represent the cotangent function in terms of the secant function using trig identities, cot 90° can be written as 1/√(sec²(90°) - 1). 

How to Find the Value of Cot 90 Degrees?

The value of cot 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 cot 90° is equal to the x-coordinate(0) divided by the y-coordinate (1). ∴ cot 90° = 0

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

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

• cos(90°)/sin(90°)
• ± cos 90°/√(1 - cos²(90°))
• ± √(1 - sin²(90°))/sin 90°
• ± 1/√(sec²(90°) - 1)
• ± √(cosec²(90°) - 1)
• 1/tan 90°

☛ Also check: trigonometric table

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

Using trigonometric identities, we can write cot 90° in terms of sin 90° as, cot(90°) = √(1 - sin²(90°))/sin 90° . Here, the value of sin 90° is equal to 1.