The value of cos pi/12 is 0.9659258. . .
You are watching: Cos(-pi/12)
. Cos pi/12 radians in degrees is written as cos ((π/12) × 180°/π), i.e., cos (15°). In this article, we will discuss the methods to discover the worth of cos pi/12 v examples.
What is the value of Cos pi/12?
The value of cos pi/12 in decimal is 0.965925826. . .. Cos pi/12 can additionally be expressed utilizing the indistinguishable of the given angle (pi/12) in levels (15°).
We know, using radian to level conversion, θ in levels = θ in radians × (180°/pi)⇒ pi/12 radians = pi/12 × (180°/pi) = 15° or 15 degrees∴ cos pi/12 = cos π/12 = cos(15°) = (√6 + √2)/4 or 0.9659258. . .
For cos pi/12, the edge pi/12 lies in between 0 and pi/2 (First Quadrant). Due to the fact that cosine role is confident in the an initial quadrant, hence cos pi/12 worth = (√6 + √2)/4 or 0.9659258. . .Since the cosine role is a regular function, we have the right to represent cos pi/12 as, cos pi/12 = cos(pi/12 + n × 2pi), n ∈ Z.⇒ cos pi/12 = cos 25pi/12 = cos 49pi/12 , and so on.Note: Since, cosine is an even function, the value of cos(-pi/12) = cos(pi/12).
Methods to discover Value that Cos pi/12
The cosine role is optimistic in the 1st quadrant. The worth of cos pi/12 is given as 0.96592. . .. We can find the worth of cos pi/12 by:Using Trigonometric FunctionsUsing Unit Circle
Cos pi/12 in terms of Trigonometric Functions
Using trigonometry formulas, we have the right to represent the cos pi/12 as:± √(1-sin²(pi/12))± 1/√(1 + tan²(pi/12))± cot(pi/12)/√(1 + cot²(pi/12))±√(cosec²(pi/12) - 1)/cosec(pi/12)1/sec(pi/12)
Note: due to the fact that pi/12 lies in the first Quadrant, the final value of cos pi/12 will certainly be positive.
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We can use trigonometric identities to stand for cos pi/12 as,-cos(pi - pi/12) = -cos 11pi/12-cos(pi + pi/12) = -cos 13pi/12sin(pi/2 + pi/12) = sin 7pi/12sin(pi/2 - pi/12) = sin 5pi/12
Cos pi/12 making use of Unit Circle
To find the value of cos π/12 using the unit circle:Rotate ‘r’ anticlockwise to type pi/12 angle through the optimistic x-axis.The cos the pi/12 equates to the x-coordinate(0.9659) the the allude of intersection (0.9659, 0.2588) the unit circle and r.
Hence the value of cos pi/12 = x = 0.9659 (approx)