The value of cot pi/2 is 0. Cot pi/2 radians in degrees is written as cot ((π/2) × 180°/π), i.e., cot (90°). In this article, we will discuss the methods to find the value of cot pi/2 with examples.
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What is the Value of Cot pi/2?
The value of cot pi/2 is 0. Cot pi/2 can also be expressed using the equivalent of the given angle (pi/2) in degrees (90°).
We know, using radian khổng lồ degree conversion, θ in degrees = θ in radians × (180°/pi)⇒ pi/2 radians = pi/2 × (180°/pi) = 90° or 90 degrees∴ cot pi/2 = cot π/2 = cot(90°) = 0
Explanation:
For cot pi/2, the angle pi/2 lies on the positive y-axis. Thus, cot pi/2 value = 0Since the cotangent function is a periodic function, we can represent cot pi/2 as, cot pi/2 = cot(pi/2 + n × pi), n ∈ Z.⇒ cot pi/2 = cot 3pi/2 = cot 5pi/2 , và so on.Note: Since, cotangent is an odd function, the value of cot(-pi/2) = -cot(pi/2) = 0.
Methods to lớn Find Value of Cot pi/2
The value of cot pi/2 is given as 0. We can find the value of cot pi/2 by:
Using Unit CircleUsing Trigonometric FunctionsCot pi/2 Using Unit Circle
To find the value of cot π/2 using the unit circle:
Rotate ‘r’ anticlockwise to khung pi/2 angle with the positive x-axis.The cot of pi/2 equals the x-coordinate(0) divided by y-coordinate(1) of the point of intersection (0, 1) of unit circle và r.Hence the value of cot pi/2 = x/y = 0
Cot pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cot pi/2 as:
cos(pi/2)/sin(pi/2)± cos(pi/2)/√(1 - cos²(pi/2))± √(1 - sin²(pi/2))/sin(pi/2)± 1/√(sec²(pi/2) - 1)± √(cosec²(pi/2) - 1)1/tan(pi/2)Note: Since pi/2 lies on the positive y-axis, the final value of cot pi/2 is 0.
We can use trigonometric identities to represent cot pi/2 as,
tan (pi/2 - pi/2) = rã 0-tan (pi/2 + pi/2) = -tan pi-cot (pi - pi/2) = -cot pi/2☛ Also Check:
FAQs on Cot pi/2
What is Cot pi/2?
Cot pi/2 is the value of cotangent trigonometric function for an angle equal khổng lồ π/2 radians. The value of cot pi/2 is 0.
How to lớn Find Cot pi/2 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cot pi/2 can be given in terms of other trigonometric functions as:
cos(pi/2)/sin(pi/2)± cos(pi/2)/√(1 - cos²(pi/2))± √(1 - sin²(pi/2))/sin(pi/2)± 1/√(sec²(pi/2) - 1)± √(cosec²(pi/2) - 1)1/tan(pi/2)☛ Also check: trigonometry table
What is the Value of Cot pi/2 in Terms of Cos pi/2?
We know, using trig identities, we can write cot pi/2 as cos(pi/2)/√(1 - cos²(pi/2)). Here, the value of cos pi/2 is equal to 0.
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How khổng lồ Find the Value of Cot pi/2?
The value of cot pi/2 can be calculated by constructing an angle of π/2 radians with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cot pi/2 is equal to lớn the x-coordinate(0) divided by the y-coordinate (1). ∴ cot pi/2 = 0
What is the Value of Cot pi/2 in Terms of Cosec pi/2?
Since the cotangent function can be represented using the cosecant function, we can write cot pi/2 as √(cosec²(pi/2) - 1). The value of cosec pi/2 is equal lớn 1.