The worth of cos 7pi/12 is -0.2588190. . .
You are watching: Cos 7pi/12 exact value
. Cos 7pi/12 radians in levels is composed as cos ((7π/12) × 180°/π), i.e., cos (105°). In this article, we will comment on the approaches to discover the worth of cos 7pi/12 through examples.
What is the worth of Cos 7pi/12?
The value of cos 7pi/12 in decimal is -0.258819045. . .. Cos 7pi/12 can also be expressed making use of the indistinguishable of the provided angle (7pi/12) in levels (105°).
We know, utilizing radian to degree conversion, θ in degrees = 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. . .
For cos 7pi/12, the edge 7pi/12 lies in between pi/2 and pi (Second Quadrant). Due to the fact that cosine function is an unfavorable in the second quadrant, for this reason cos 7pi/12 worth = -(√6-√2)/4 or -0.2588190. . .Since the cosine function is a periodic function, we have the right to 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 worth of cos(-7pi/12) = cos(7pi/12).
Methods to discover Value that Cos 7pi/12
The cosine role is an unfavorable in the 2nd quadrant. The value of cos 7pi/12 is given as -0.25881. . .. We can find the worth of cos 7pi/12 by:Using Unit CircleUsing Trigonometric Functions
Cos 7pi/12 utilizing Unit Circle
To find the value of cos 7π/12 utilizing the unit circle:Rotate ‘r’ anticlockwise to kind 7pi/12 angle through the optimistic x-axis.The cos that 7pi/12 equates to the x-coordinate(-0.2588) that the allude of intersection (-0.2588, 0.9659) of unit circle and also r.
Hence the worth of cos 7pi/12 = x = -0.2588 (approx)
Cos 7pi/12 in terms of Trigonometric Functions
Using trigonometry formulas, we can 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: due to the fact that 7pi/12 lies in the 2nd Quadrant, the last value of cos 7pi/12 will be negative.
We deserve to use trigonometric identities to represent 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)
☛ additionally Check:
FAQs on Cos 7pi/12
What is Cos 7pi/12?
Cos 7pi/12 is the value of cosine trigonometric function for one angle equal to 7π/12 radians. The worth of cos 7pi/12 is -(√6-√2)/4 or -0.2588 (approx)
How to discover Cos 7pi/12 in state of other Trigonometric Functions?
Using trigonometry formula, the value of cos 7pi/12 deserve to be provided in state of other trigonometric features 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)
☛ also check: trigonometric table
What is the value of Cos 7pi/12 in regards to Cot 7pi/12?
We can represent the cosine role in regards to the cotangent function using trig identities, cos 7pi/12 can be composed as cot(7pi/12)/√(1 + cot²(7pi/12)). Here, the value of cot 7pi/12 is equal to -0.26794.
How to find the value of Cos 7pi/12?
The worth of cos 7pi/12 deserve to be calculated by creating an angle of 7π/12 radians v the x-axis, and then finding the collaborates of the corresponding point (-0.2588, 0.9659) on the unit circle. The value of cos 7pi/12 is same to the x-coordinate (-0.2588). ∴ cos 7pi/12 = -0.2588.
See more: How Do You Say Jeff In Spanish, How To Pronounce Jeff In Spanish (1 Out Of 327)
What is the worth of Cos 7pi/12 in regards to Sec 7pi/12?
Since the secant role is the reciprocal of the cosine function, we deserve to write cos 7pi/12 as 1/sec(7pi/12). The value of sec 7pi/12 is same to -3.863703.