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.

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.

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

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

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,

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

Hence the value of cot 90° = x/y = 0

☛ Also Check:

Example 1: Simplify: 5 (cot 90°/tan 45°)

Solution:

We know cot 90° = 0 and tan 45° = 1 ⇒ 5 cot 90°/tan 45° = 5(0) = 0

Example 2: Find the value of (cos (90°) cosec (45°) sec (45°))/2. [Hint: Use cot 90° = 0]

Solution:

Using trigonometry formulas, (cos (90°) cosec (45°) sec (45°))/2 = cos (90°)/(2 sin (45°) cos (45°)) Using sin 2a formula, 2 sin (45°) cos (45°) = sin (2 × 45°) = sin 90° ⇒ cos (90°) / sin (90°) = cot 90° ⇒ (cos (90°) cosec (45°) sec (45°))/2 = 0

Example 3: Find the value of 2 cot(90°)/7 sin(90°).

Solution:

Using trigonometric identities, we know, cot(90°) = 0 and sin 90° = 1. ⇒ Value of 2 cot(90°)/7 sin(90°) = 0

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

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). 

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

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

☛ Also check: trigonometric table

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.