Cos 245 Degrees

The value of cos 245 degrees is -0.4226182. . .. Cos 245 degrees in radians is written as cos (245° × π/180°), i.e., cos (49π/36) or cos (4.276056. . .). In this article, we will discuss the methods to find the value of cos 245 degrees with examples.

• Cos 245°: -0.4226182. . .
• Cos (-245 degrees): -0.4226182. . .
• Cos 245° in radians: cos (49π/36) or cos (4.2760566 . . .)

What is the Value of Cos 245 Degrees?

The value of cos 245 degrees in decimal is -0.422618261. . .. Cos 245 degrees can also be expressed using the equivalent of the given angle (245 degrees) in radians (4.27605 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 245 degrees = 245° × (π/180°) rad = 49π/36 or 4.2760 . . .
∴ cos 245° = cos(4.2760) = -0.4226182. . .

Explanation:

For cos 245 degrees, the angle 245° lies between 180° and 270° (Third Quadrant). Since cosine function is negative in the third quadrant, thus cos 245° value = -0.4226182. . .
Since the cosine function is a periodic function, we can represent cos 245° as, cos 245 degrees = cos(245° + n × 360°), n ∈ Z.
⇒ cos 245° = cos 605° = cos 965°, and so on.
Note: Since, cosine is an even function, the value of cos(-245°) = cos(245°).

Methods to Find Value of Cos 245 Degrees

The cosine function is negative in the 3rd quadrant. The value of cos 245° is given as -0.42261. . .. We can find the value of cos 245 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 245 Degrees Using Unit Circle

To find the value of cos 245 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 245° angle with the positive x-axis.
• The cos of 245 degrees equals the x-coordinate(-0.4226) of the point of intersection (-0.4226, -0.9063) of unit circle and r.

Hence the value of cos 245° = x = -0.4226 (approx)

Cos 245° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 245 degrees as:

• ± √(1-sin²(245°))
• ± 1/√(1 + tan²(245°))
• ± cot 245°/√(1 + cot²(245°))
• ±√(cosec²(245°) - 1)/cosec 245°
• 1/sec 245°

Note: Since 245° lies in the 3rd Quadrant, the final value of cos 245° will be negative.

We can use trigonometric identities to represent cos 245° as,

• -cos(180° - 245°) = -cos(-65°)
• -cos(180° + 245°) = -cos 425°
• sin(90° + 245°) = sin 335°
• sin(90° - 245°) = sin(-155°)

☛ Also Check:

• cos 240 degrees
• cos 45 degrees
• cos 37 degrees
• cos 106 degrees
• cos 145 degrees
• cos 42 degrees

FAQs on Cos 245 Degrees

What is Cos 245 Degrees?

Cos 245 degrees is the value of cosine trigonometric function for an angle equal to 245 degrees. The value of cos 245° is -0.4226 (approx)

How to Find the Value of Cos 245 Degrees?

The value of cos 245 degrees can be calculated by constructing an angle of 245° with the x-axis, and then finding the coordinates of the corresponding point (-0.4226, -0.9063) on the unit circle. The value of cos 245° is equal to the x-coordinate (-0.4226). ∴ cos 245° = -0.4226.

What is the Value of Cos 245 Degrees in Terms of Tan 245°?

We know, using trig identities, we can write cos 245° as -1/√(1 + tan²(245°)). Here, the value of tan 245° is equal to 2.144506.

How to Find Cos 245° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 245° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(245°))
• ± 1/√(1 + tan²(245°))
• ± cot 245°/√(1 + cot²(245°))
• ± √(cosec²(245°) - 1)/cosec 245°
• 1/sec 245°

☛ Also check: trigonometry table

What is the Value of Cos 245° in Terms of Cosec 245°?

Since the cosine function can be represented using the cosecant function, we can write cos 245° as [√(cosec²(245°) - 1)/cosec 245°]. The value of cosec 245° is equal to -1.10337.