Cos 230 Degrees

The value of cos 230 degrees is -0.6427876. . .. Cos 230 degrees in radians is written as cos (230° × π/180°), i.e., cos (23π/18) or cos (4.014257. . .). In this article, we will discuss the methods to find the value of cos 230 degrees with examples.

• Cos 230°: -0.6427876. . .
• Cos (-230 degrees): -0.6427876. . .
• Cos 230° in radians: cos (23π/18) or cos (4.0142572 . . .)

What is the Value of Cos 230 Degrees?

The value of cos 230 degrees in decimal is -0.642787609. . .. Cos 230 degrees can also be expressed using the equivalent of the given angle (230 degrees) in radians (4.01425 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 230 degrees = 230° × (π/180°) rad = 23π/18 or 4.0142 . . .
∴ cos 230° = cos(4.0142) = -0.6427876. . .

Explanation:

For cos 230 degrees, the angle 230° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 230° value = -0.6427876. . .
Since the cosine function is a periodic function, we can represent cos 230° as, cos 230 degrees = cos(230° + n × 360°), n ∈ Z.
⇒ cos 230° = cos 590° = cos 950°, and so on.
Note: Since, cosine is an even function, the value of cos(-230°) = cos(230°).

Methods to Find Value of Cos 230 Degrees

The cosine function is negative in the 3rd quadrant. The value of cos 230° is given as -0.64278. . .. We can find the value of cos 230 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 230 Degrees Using Unit Circle

To find the value of cos 230 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 230° angle with the positive x-axis.
• The cos of 230 degrees equals the x-coordinate(-0.6428) of the point of intersection (-0.6428, -0.766) of unit circle and r.

Hence the value of cos 230° = x = -0.6428 (approx)

Cos 230° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 230 degrees as:

• ± √(1-sin²(230°))
• ± 1/√(1 + tan²(230°))
• ± cot 230°/√(1 + cot²(230°))
• ±√(cosec²(230°) - 1)/cosec 230°
• 1/sec 230°

Note: Since 230° lies in the 3rd Quadrant, the final value of cos 230° will be negative.

We can use trigonometric identities to represent cos 230° as,

• -cos(180° - 230°) = -cos(-50°)
• -cos(180° + 230°) = -cos 410°
• sin(90° + 230°) = sin 320°
• sin(90° - 230°) = sin(-140°)

☛ Also Check:

• cos 120 degrees
• cos 11 degrees
• cos 15 degrees
• cos 340 degrees
• cos 24 degrees
• cos 8 degrees

FAQs on Cos 230 Degrees

What is Cos 230 Degrees?

Cos 230 degrees is the value of cosine trigonometric function for an angle equal to 230 degrees. The value of cos 230° is -0.6428 (approx)

How to Find the Value of Cos 230 Degrees?

The value of cos 230 degrees can be calculated by constructing an angle of 230° with the x-axis, and then finding the coordinates of the corresponding point (-0.6428, -0.766) on the unit circle. The value of cos 230° is equal to the x-coordinate (-0.6428). ∴ cos 230° = -0.6428.

What is the Value of Cos 230 Degrees in Terms of Sin 230°?

Using trigonometric identities, we can write cos 230° in terms of sin 230° as, cos(230°) = -√(1 - sin²(230°)). Here, the value of sin 230° is equal to -0.766.

How to Find Cos 230° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 230° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(230°))
• ± 1/√(1 + tan²(230°))
• ± cot 230°/√(1 + cot²(230°))
• ± √(cosec²(230°) - 1)/cosec 230°
• 1/sec 230°

☛ Also check: trigonometric table

What is the Value of Cos 230° in Terms of Cosec 230°?

Since the cosine function can be represented using the cosecant function, we can write cos 230° as [√(cosec²(230°) - 1)/cosec 230°]. The value of cosec 230° is equal to -1.30540.