The value of cos pi/2 is 0. Cos pi/2 radians in degrees is written as cos ((π/2) × 180°/π), i.e., cos (90°). In this article, we will discuss the methods khổng lồ find the value of cos pi/2 with examples.
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What is the Value of Cos pi/2?
The value of cos pi/2 is 0. Cos 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∴ cos pi/2 = cos π/2 = cos(90°) = 0
Explanation:
For cos pi/2, the angle pi/2 lies on the positive y-axis. Thus, cos pi/2 value = 0Since the cosine function is a periodic function, we can represent cos pi/2 as, cos pi/2 = cos(pi/2 + n × 2pi), n ∈ Z.⇒ cos pi/2 = cos 5pi/2 = cos 9pi/2 , & so on.Note: Since, cosine is an even function, the value of cos(-pi/2) = cos(pi/2) = 0.
Methods to Find Value of Cos pi/2
The value of cos pi/2 is given as 0.We can find the value of cos pi/2 by:
Using Trigonometric FunctionsUsing Unit CircleCos pi/2 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the cos pi/2 as:
± √(1-sin²(pi/2))± 1/√(1 + tan²(pi/2))± cot(pi/2)/√(1 + cot²(pi/2))±√(cosec²(pi/2) - 1)/cosec(pi/2)1/sec(pi/2)Note: Since pi/2 lies on the positive y-axis, the final value of cos pi/2 is 0.
We can use trigonometric identities to lớn represent cos pi/2 as,
-cos(pi - pi/2) = -cos pi/2-cos(pi + pi/2) = -cos 3pi/2sin(pi/2 + pi/2) = sin pisin(pi/2 - pi/2) = sin 0Cos pi/2 Using Unit Circle
To find the value of cos π/2 using the unit circle:
Rotate ‘r’ anticlockwise to size pi/2 angle with the positive x-axis.The cos of pi/2 equals the x-coordinate(0) of the point of intersection (0, 1) of unit circle & r.Hence the value of cos pi/2 = x = 0
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FAQs on Cos pi/2
What is Cos pi/2?
Cos pi/2 is the value of cosine trigonometric function for an angle equal khổng lồ π/2 radians. The value of cos pi/2 is 0.
What is the Value of Cos pi/2 in Terms of chảy pi/2?
We know, using trig identities, we can write cos pi/2 as 1/√(1 + tan²(pi/2)).
How to lớn Find Cos pi/2 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of cos pi/2 can be given in terms of other trigonometric functions as:
± √(1-sin²(pi/2))± 1/√(1 + tan²(pi/2))± cot(pi/2)/√(1 + cot²(pi/2))±√(cosec²(pi/2) - 1)/cosec(pi/2)1/sec(pi/2)☛ Also check: trigonometry table
How khổng lồ Find the Value of Cos pi/2?
The value of cos pi/2 can be calculated by constructing an angle of π/2 radians with the x-axis, & then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cos pi/2 is equal lớn the x-coordinate (0). ∴ cos pi/2 = 0.
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What is the Value of Cos pi/2 in Terms of Cosec pi/2?
Since the cosine function can be represented using the cosecant function, we can write cos pi/2 as <√(cosec²(pi/2) - 1)/cosec pi/2>. The value of cosec pi/2 is equal khổng lồ 1.