The value of cos 7pi/12 is -0.2588190. . .
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. Cos 7pi/12 radians in degrees is composed as cos ((7π/12) × 180°/π), i.e., cos (105°). In this article, we will discuss the techniques to discover the value of cos 7pi/12 v examples.
What is the value of Cos 7pi/12?
The value of cos 7pi/12 in decimal is -0.258819045. . .. Cos 7pi/12 can likewise be expressed using the tantamount of the provided angle (7pi/12) in degrees (105°).
We know, making use of radian to level conversion, θ in levels = θ in radians × (180°/pi)⇒ 7pi/12 radians = 7pi/12 × (180°/pi) = 105° or 105 degrees∴ cos 7pi/12 = cos 7π/12 = cos(105°) = -(√6-√2)/4 or -0.2588190. . .
Explanation:
For cos 7pi/12, the angle 7pi/12 lies in between pi/2 and pi (Second Quadrant). Because cosine function is an adverse in the 2nd quadrant, hence cos 7pi/12 worth = -(√6-√2)/4 or -0.2588190. . .Since the cosine duty is a periodic function, we can represent cos 7pi/12 as, cos 7pi/12 = cos(7pi/12 + n × 2pi), n ∈ Z.⇒ cos 7pi/12 = cos 31pi/12 = cos 55pi/12 , and also so on.Note: Since, cosine is an even function, the value of cos(-7pi/12) = cos(7pi/12).
Methods to discover Value of Cos 7pi/12
The cosine function is an adverse in the second quadrant. The value of cos 7pi/12 is provided as -0.25881. . .. Us can find the worth of cos 7pi/12 by:
Using Unit CircleUsing Trigonometric FunctionsCos 7pi/12 making use of Unit Circle
To find the worth of cos 7π/12 utilizing the unit circle:
Rotate ‘r’ anticlockwise to form 7pi/12 angle with the confident x-axis.The cos the 7pi/12 equals the x-coordinate(-0.2588) the the point of intersection (-0.2588, 0.9659) that unit circle and r.Hence the value of cos 7pi/12 = x = -0.2588 (approx)
Cos 7pi/12 in regards to Trigonometric Functions
Using trigonometry formulas, we have the right to represent the cos 7pi/12 as:
± √(1-sin²(7pi/12))± 1/√(1 + tan²(7pi/12))± cot(7pi/12)/√(1 + cot²(7pi/12))±√(cosec²(7pi/12) - 1)/cosec(7pi/12)1/sec(7pi/12)Note: since 7pi/12 lies in the second Quadrant, the last value of cos 7pi/12 will be negative.
We have the right to use trigonometric identities to stand for cos 7pi/12 as,
-cos(pi - 7pi/12) = -cos 5pi/12-cos(pi + 7pi/12) = -cos 19pi/12sin(pi/2 + 7pi/12) = sin 13pi/12sin(pi/2 - 7pi/12) = sin(-pi/12)☛ also Check:
FAQs top top Cos 7pi/12
What is Cos 7pi/12?
Cos 7pi/12 is the worth of cosine trigonometric duty for one angle equal to 7π/12 radians. The value of cos 7pi/12 is -(√6-√2)/4 or -0.2588 (approx)
How to discover Cos 7pi/12 in terms of other Trigonometric Functions?
Using trigonometry formula, the value of cos 7pi/12 have the right to be offered in terms of other trigonometric functions as:
± √(1-sin²(7pi/12))± 1/√(1 + tan²(7pi/12))± cot(7pi/12)/√(1 + cot²(7pi/12))±√(cosec²(7pi/12) - 1)/cosec(7pi/12)1/sec(7pi/12)☛ likewise check: trigonometric table
What is the value of Cos 7pi/12 in regards to Cot 7pi/12?
We deserve to represent the cosine role in terms of the cotangent role using trig identities, cos 7pi/12 deserve to be written as cot(7pi/12)/√(1 + cot²(7pi/12)). Here, the worth of cot 7pi/12 is equal to -0.26794.
How to discover the worth of Cos 7pi/12?
The value of cos 7pi/12 have the right to be calculate by creating an angle of 7π/12 radians with the x-axis, and then detect the works with of the corresponding allude (-0.2588, 0.9659) on the unit circle. The worth of cos 7pi/12 is equal to the x-coordinate (-0.2588). ∴ cos 7pi/12 = -0.2588.
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What is the worth of Cos 7pi/12 in regards to Sec 7pi/12?
Since the secant duty is the mutual of the cosine function, we can write cos 7pi/12 together 1/sec(7pi/12). The value of sec 7pi/12 is same to -3.863703.