The value of cos pi/2 is 0. Cos pi/2 radians in degrees is composed as cos ((π/2) × 180°/π), i.e., cos (90°). In this article, us will discuss the techniques to discover the value of cos pi/2 through examples.
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What is the value of Cos pi/2?
The worth of cos pi/2 is 0. Cos pi/2 can also be expressed utilizing the tantamount of the provided angle (pi/2) in levels (90°).
We know, utilizing radian to level 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
For cos pi/2, the edge pi/2 lies top top the positive y-axis. Thus, cos pi/2 worth = 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 , and so on.Note: Since, cosine is an also function, the value of cos(-pi/2) = cos(pi/2) = 0.
Methods to uncover Value of Cos pi/2
The value of cos pi/2 is given as 0.We can find the worth of cos pi/2 by:Using Trigonometric FunctionsUsing Unit Circle
Cos pi/2 in regards to Trigonometric Functions
Using trigonometry formulas, we deserve to 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: because pi/2 lies on the optimistic y-axis, the final value the cos pi/2 is 0.
We deserve to use trigonometric identities to stand for 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 0
Cos pi/2 making use of Unit Circle
To find the value of cos π/2 utilizing the unit circle:Rotate ‘r’ anticlockwise to form pi/2 angle with the optimistic x-axis.The cos that pi/2 equals the x-coordinate(0) of the allude of intersection (0, 1) of unit circle and also r.
Hence the value of cos pi/2 = x = 0
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FAQs top top Cos pi/2
What is Cos pi/2?
Cos pi/2 is the value of cosine trigonometric function for an angle same to π/2 radians. The worth of cos pi/2 is 0.
What is the worth of Cos pi/2 in regards to Tan pi/2?
We know, making use of trig identities, we deserve to write cos pi/2 as 1/√(1 + tan²(pi/2)).
How to uncover Cos pi/2 in state of various other Trigonometric Functions?
Using trigonometry formula, the value of cos pi/2 can be provided in terms of various other trigonometric features 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)
☛ likewise check: trigonometry table
How to discover the value of Cos pi/2?
The worth of cos pi/2 can be calculation by constructing an edge of π/2 radians v the x-axis, and then recognize the works with of the corresponding suggest (0, 1) ~ above the unit circle. The worth of cos pi/2 is equal to the x-coordinate (0). ∴ cos pi/2 = 0.
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What is the worth of Cos pi/2 in regards to Cosec pi/2?
Since the cosine role can be stood for using the cosecant function, we can write cos pi/2 together <√(cosec²(pi/2) - 1)/cosec pi/2>. The value of cosec pi/2 is same to 1.