Cos 250 Degrees

The value of cos 250 degrees is -0.3420201. . .. Cos 250 degrees in radians is written as cos (250° × π/180°), i.e., cos (25π/18) or cos (4.363323. . .). In this article, we will discuss the methods to find the value of cos 250 degrees with examples.

• Cos 250°: -0.3420201. . .
• Cos (-250 degrees): -0.3420201. . .
• Cos 250° in radians: cos (25π/18) or cos (4.3633231 . . .)

What is the Value of Cos 250 Degrees?

The value of cos 250 degrees in decimal is -0.342020143. . .. Cos 250 degrees can also be expressed using the equivalent of the given angle (250 degrees) in radians (4.36332 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 250 degrees = 250° × (π/180°) rad = 25π/18 or 4.3633 . . .
∴ cos 250° = cos(4.3633) = -0.3420201. . .

Explanation:

For cos 250 degrees, the angle 250° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 250° value = -0.3420201. . .
Since the cosine function is a periodic function, we can represent cos 250° as, cos 250 degrees = cos(250° + n × 360°), n ∈ Z.
⇒ cos 250° = cos 610° = cos 970°, and so on.
Note: Since, cosine is an even function, the value of cos(-250°) = cos(250°).

Methods to Find Value of Cos 250 Degrees

The cosine function is negative in the 3rd quadrant. The value of cos 250° is given as -0.34202. . .. We can find the value of cos 250 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 250° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 250 degrees as:

• ± √(1-sin²(250°))
• ± 1/√(1 + tan²(250°))
• ± cot 250°/√(1 + cot²(250°))
• ±√(cosec²(250°) - 1)/cosec 250°
• 1/sec 250°

Note: Since 250° lies in the 3rd Quadrant, the final value of cos 250° will be negative.

We can use trigonometric identities to represent cos 250° as,

• -cos(180° - 250°) = -cos(-70°)
• -cos(180° + 250°) = -cos 430°
• sin(90° + 250°) = sin 340°
• sin(90° - 250°) = sin(-160°)

Cos 250 Degrees Using Unit Circle

To find the value of cos 250 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 250° angle with the positive x-axis.
• The cos of 250 degrees equals the x-coordinate(-0.342) of the point of intersection (-0.342, -0.9397) of unit circle and r.

Hence the value of cos 250° = x = -0.342 (approx)

☛ Also Check:

• cos 3 degrees
• cos 225 degrees
• cos 360 degrees
• cos 405 degrees
• cos 540 degrees
• cos 66 degrees

FAQs on Cos 250 Degrees

What is Cos 250 Degrees?

Cos 250 degrees is the value of cosine trigonometric function for an angle equal to 250 degrees. The value of cos 250° is -0.342 (approx)

How to Find the Value of Cos 250 Degrees?

The value of cos 250 degrees can be calculated by constructing an angle of 250° with the x-axis, and then finding the coordinates of the corresponding point (-0.342, -0.9397) on the unit circle. The value of cos 250° is equal to the x-coordinate (-0.342). ∴ cos 250° = -0.342.

What is the Value of Cos 250 Degrees in Terms of Tan 250°?

We know, using trig identities, we can write cos 250° as -1/√(1 + tan²(250°)). Here, the value of tan 250° is equal to 2.747477.

What is the Value of Cos 250° in Terms of Cosec 250°?

Since the cosine function can be represented using the cosecant function, we can write cos 250° as [√(cosec²(250°) - 1)/cosec 250°]. The value of cosec 250° is equal to -1.06417.

How to Find Cos 250° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 250° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(250°))
• ± 1/√(1 + tan²(250°))
• ± cot 250°/√(1 + cot²(250°))
• ± √(cosec²(250°) - 1)/cosec 250°
• 1/sec 250°

☛ Also check: trigonometry table