Cos 7pi/6

The value of cos 7pi/6 is -0.8660254. . .. Cos 7pi/6 radians in degrees is written as cos ((7π/6) × 180°/π), i.e., cos (210°). In this article, we will discuss the methods to find the value of cos 7pi/6 with examples.

• Cos 7pi/6: -√(3)/2
• Cos 7pi/6 in decimal: -0.8660254. . .
• Cos (-7pi/6): -0.8660254. . . or −√3/2
• Cos 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 also be expressed using the equivalent of the given angle (7pi/6) in degrees (210°).

We know, using radian to degree conversion, θ in degrees = 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. . .

Explanation:

For cos 7pi/6, the angle 7pi/6 lies between pi and 3pi/2 (Third Quadrant). Since cosine function is negative in the third quadrant, thus 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 so on.
Note: Since, cosine is an even function, the value of cos(-7pi/6) = cos(7pi/6).

Methods to Find Value of 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 find the value of cos 7pi/6 by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 7pi/6 Using Unit Circle

To find the value of cos 7π/6 using the unit circle:

• Rotate ‘r’ anticlockwise to form 7pi/6 angle with the positive x-axis.
• The cos of 7pi/6 equals the x-coordinate(-0.866) of the point of intersection (-0.866, -0.5) of unit circle and r.

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

Cos 7pi/6 in Terms of 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 final value of cos 7pi/6 will be negative.

We can use trigonometric identities to represent cos 7pi/6 as,

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

☛ Also Check:

• cos 2pi
• tan pi/12
• tan 4pi/3
• sin 2pi
• sin 11pi/12
• sin 11pi/6

FAQs on Cos 7pi/6

What is Cos 7pi/6?

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

What is the Value of Cos 7pi/6 in Terms of Sec 7pi/6?

Since the secant function is the reciprocal of the cosine function, we can write cos 7pi/6 as 1/sec(7pi/6). The value of sec 7pi/6 is equal to -1.154700.

What is the Value of Cos 7pi/6 in Terms of Cot 7pi/6?

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

How to Find the Value of Cos 7pi/6?

The value of cos 7pi/6 can be calculated by constructing an angle of 7π/6 radians with the x-axis, and then finding the coordinates of the corresponding point (-0.866, -0.5) on the unit circle. The value of cos 7pi/6 is equal to the x-coordinate (-0.866). ∴ cos 7pi/6 = -0.866.

How to Find Cos 7pi/6 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 7pi/6 can be given in terms 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