Cos 210 Degrees

The value of cos 210 degrees is -0.8660254. . .. Cos 210 degrees in radians is written as cos (210° × π/180°), i.e., cos (7π/6) or cos (3.665191. . .). In this article, we will discuss the methods to find the value of cos 210 degrees with examples.

• Cos 210°: -0.8660254. . .
• Cos 210° in fraction: -√(3)/2
• Cos (-210 degrees): -0.8660254. . .
• Cos 210° in radians: cos (7π/6) or cos (3.6651914 . . .)

What is the Value of Cos 210 Degrees?

The value of cos 210 degrees in decimal is -0.866025403. . .. Cos 210 degrees can also be expressed using the equivalent of the given angle (210 degrees) in radians (3.66519 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 210 degrees = 210° × (π/180°) rad = 7π/6 or 3.6651 . . .
∴ cos 210° = cos(3.6651) = -√(3)/2 or -0.8660254. . .

Explanation:

For cos 210 degrees, the angle 210° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 210° value = -√(3)/2 or -0.8660254. . .
Since the cosine function is a periodic function, we can represent cos 210° as, cos 210 degrees = cos(210° + n × 360°), n ∈ Z.
⇒ cos 210° = cos 570° = cos 930°, and so on.
Note: Since, cosine is an even function, the value of cos(-210°) = cos(210°).

Methods to Find Value of Cos 210 Degrees

The cosine function is negative in the 3rd quadrant. The value of cos 210° is given as -0.86602. . .. We can find the value of cos 210 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 210 Degrees Using Unit Circle

To find the value of cos 210 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 210° angle with the positive x-axis.
• The cos of 210 degrees 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 210° = x = -0.866 (approx)

Cos 210° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 210 degrees as:

• ± √(1-sin²(210°))
• ± 1/√(1 + tan²(210°))
• ± cot 210°/√(1 + cot²(210°))
• ±√(cosec²(210°) - 1)/cosec 210°
• 1/sec 210°

Note: Since 210° lies in the 3rd Quadrant, the final value of cos 210° will be negative.

We can use trigonometric identities to represent cos 210° as,

• -cos(180° - 210°) = -cos(-30°)
• -cos(180° + 210°) = -cos 390°
• sin(90° + 210°) = sin 300°
• sin(90° - 210°) = sin(-120°)

☛ Also Check:

• cos 360 degrees
• cos 60 degrees
• cos 11 degrees
• cos 106 degrees
• cos 23 degrees
• cos 72 degrees

FAQs on Cos 210 Degrees

What is Cos 210 Degrees?

Cos 210 degrees is the value of cosine trigonometric function for an angle equal to 210 degrees. The value of cos 210° is -√(3)/2 or -0.866 (approx)

What is the Value of Cos 210 Degrees in Terms of Tan 210°?

We know, using trig identities, we can write cos 210° as -1/√(1 + tan²(210°)). Here, the value of tan 210° is equal to 0.577350.

How to Find the Value of Cos 210 Degrees?

The value of cos 210 degrees can be calculated by constructing an angle of 210° 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 210° is equal to the x-coordinate (-0.866). ∴ cos 210° = -0.866.

How to Find Cos 210° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 210° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(210°))
• ± 1/√(1 + tan²(210°))
• ± cot 210°/√(1 + cot²(210°))
• ± √(cosec²(210°) - 1)/cosec 210°
• 1/sec 210°

☛ Also check: trigonometric table

What is the Exact Value of cos 210 Degrees?

The exact value of cos 210 degrees can be given accurately up to 8 decimal places as -0.86602540 and -√(3)/2 in fraction.