from a handpicked tutor in LIVE 1to1 classes
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 yaxis. 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 yaxis, 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 xaxis.
 The cot of 90 degrees equals the xcoordinate(0) divided by ycoordinate(1) of the point of intersection (0, 1) of unit circle and r.
Hence the value of cot 90° = x/y = 0
☛ Also Check:
Examples Using Cot 90 Degrees

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
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 xaxis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cot 90° is equal to the xcoordinate(0) divided by the ycoordinate (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.
visual curriculum