The value of cos 7pi/6 is -0.8660254. . .

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. Cos 7pi/6 radians in levels is composed as cos ((7π/6) × 180°/π), i.e., cos (210°). In this article, us will comment on the techniques to uncover the value of cos 7pi/6 with examples.

Cos 7pi/6: -√(3)/2Cos 7pi/6 in decimal: -0.8660254. . .Cos (-7pi/6): -0.8660254. . . Or −√3/2Cos 7pi/6 in degrees: cos (210°)

What is the value of Cos 7pi/6?

The value of cos 7pi/6 in decimal is -0.866025403. . .. Cos 7pi/6 can likewise be expressed utilizing the indistinguishable of the offered angle (7pi/6) in degrees (210°).

We know, using radian to level conversion, θ in levels = θ in radians × (180°/pi)⇒ 7pi/6 radians = 7pi/6 × (180°/pi) = 210° or 210 degrees∴ cos 7pi/6 = cos 7π/6 = cos(210°) = -√(3)/2 or -0.8660254. . .

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Explanation:

For cos 7pi/6, the edge 7pi/6 lies between pi and also 3pi/2 (Third Quadrant). Because cosine duty is negative in the third quadrant, therefore cos 7pi/6 value = -√(3)/2 or -0.8660254. . .Since the cosine function is a periodic function, we can represent cos 7pi/6 as, cos 7pi/6 = cos(7pi/6 + n × 2pi), n ∈ Z.⇒ cos 7pi/6 = cos 19pi/6 = cos 31pi/6 , and also so on.Note: Since, cosine is an even function, the worth of cos(-7pi/6) = cos(7pi/6).

Methods to uncover Value the Cos 7pi/6

The cosine function is negative in the 3rd quadrant. The value of cos 7pi/6 is given as -0.86602. . .. We can discover the worth of cos 7pi/6 by:

Using Unit CircleUsing Trigonometric Functions

Cos 7pi/6 using Unit Circle

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To discover the value of cos 7π/6 utilizing the unit circle:

Rotate ‘r’ anticlockwise to type 7pi/6 angle v the positive x-axis.The cos the 7pi/6 amounts to the x-coordinate(-0.866) of the allude of intersection (-0.866, -0.5) the unit circle and also r.

Hence the worth of cos 7pi/6 = x = -0.866 (approx)

Cos 7pi/6 in regards to Trigonometric Functions

Using trigonometry formulas, we can represent the cos 7pi/6 as:

± √(1-sin²(7pi/6))± 1/√(1 + tan²(7pi/6))± cot(7pi/6)/√(1 + cot²(7pi/6))±√(cosec²(7pi/6) - 1)/cosec(7pi/6)1/sec(7pi/6)

Note: since 7pi/6 lies in the 3rd Quadrant, the last value of cos 7pi/6 will be negative.

We have the right to use trigonometric identities to stand for cos 7pi/6 as,

-cos(pi - 7pi/6) = -cos(-pi/6)-cos(pi + 7pi/6) = -cos 13pi/6sin(pi/2 + 7pi/6) = sin 5pi/3sin(pi/2 - 7pi/6) = sin(-2pi/3)

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FAQs ~ above Cos 7pi/6

What is Cos 7pi/6?

Cos 7pi/6 is the value of cosine trigonometric duty for an angle equal to 7π/6 radians. The worth of cos 7pi/6 is -√(3)/2 or -0.866 (approx)

What is the worth of Cos 7pi/6 in terms of Sec 7pi/6?

Since the secant role is the mutual of the cosine function, we have the right to write cos 7pi/6 together 1/sec(7pi/6). The value of sec 7pi/6 is equal to -1.154700.

What is the value of Cos 7pi/6 in regards to Cot 7pi/6?

We deserve to represent the cosine role in terms of the cotangent role using trig identities, cos 7pi/6 have the right to be written as -cot(7pi/6)/√(1 + cot²(7pi/6)). Here, the value of cot 7pi/6 is same to 1.73205.

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How to discover the worth of Cos 7pi/6?

The worth of cos 7pi/6 have the right to be calculation by building an edge of 7π/6 radians with the x-axis, and then finding the collaborates of the corresponding allude (-0.866, -0.5) ~ above the unit circle. The worth of cos 7pi/6 is same to the x-coordinate (-0.866). ∴ cos 7pi/6 = -0.866.

How to uncover Cos 7pi/6 in state of other Trigonometric Functions?

Using trigonometry formula, the value of cos 7pi/6 can be given in state of other trigonometric functions as:

± √(1-sin²(7pi/6))± 1/√(1 + tan²(7pi/6))± cot(7pi/6)/√(1 + cot²(7pi/6))±√(cosec²(7pi/6) - 1)/cosec(7pi/6)1/sec(7pi/6)

☛ also check: trigonometric table