The worth of cos 2pi/3 is -0.5. Cos 2pi/3 radians in degrees is composed as cos ((2π/3) × 180°/π), i.e., cos (120°). In this article, us will discuss the approaches to uncover the value of cos 2pi/3 through examples.
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What is the worth of Cos 2pi/3?
The value of cos 2pi/3 in decimal is -0.5. Cos 2pi/3 can also be expressed using the equivalent of the given angle (2pi/3) in levels (120°).
We know, utilizing radian to degree conversion, θ in levels = θ in radians × (180°/pi)⇒ 2pi/3 radians = 2pi/3 × (180°/pi) = 120° or 120 degrees∴ cos 2pi/3 = cos 2π/3 = cos(120°) = -(1/2) or -0.5
For cos 2pi/3, the edge 2pi/3 lies between pi/2 and also pi (Second Quadrant). Since cosine function is an unfavorable in the second quadrant, therefore cos 2pi/3 worth = -(1/2) or -0.5Since the cosine function is a routine function, we have the right to represent cos 2pi/3 as, cos 2pi/3 = cos(2pi/3 + n × 2pi), n ∈ Z.⇒ cos 2pi/3 = cos 8pi/3 = cos 14pi/3 , and so on.Note: Since, cosine is an even function, the value of cos(-2pi/3) = cos(2pi/3).
Methods to uncover Value that Cos 2pi/3
The cosine duty is an unfavorable in the 2nd quadrant. The worth of cos 2pi/3 is given as -0.5. Us can uncover the worth of cos 2pi/3 by:Using Unit CircleUsing Trigonometric Functions
Cos 2pi/3 utilizing Unit Circle
To find the value of cos 2π/3 using the unit circle:Rotate ‘r’ anticlockwise to kind 2pi/3 angle v the hopeful x-axis.The cos the 2pi/3 equates to the x-coordinate(-0.5) of the point of intersection (-0.5, 0.866) the unit circle and also r.
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Hence the worth of cos 2pi/3 = x = -0.5
Cos 2pi/3 in regards to Trigonometric Functions
Using trigonometry formulas, we can represent the cos 2pi/3 as:± √(1-sin²(2pi/3))± 1/√(1 + tan²(2pi/3))± cot(2pi/3)/√(1 + cot²(2pi/3))±√(cosec²(2pi/3) - 1)/cosec(2pi/3)1/sec(2pi/3)
Note: since 2pi/3 lies in the 2nd Quadrant, the final value the cos 2pi/3 will certainly be negative.
We have the right to use trigonometric identities to represent cos 2pi/3 as,-cos(pi - 2pi/3) = -cos pi/3-cos(pi + 2pi/3) = -cos 5pi/3sin(pi/2 + 2pi/3) = sin 7pi/6sin(pi/2 - 2pi/3) = sin(-pi/6)
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