Cos 115 Degrees

The value of cos 115 degrees is -0.4226182. . .. Cos 115 degrees in radians is written as cos (115° × π/180°), i.e., cos (23π/36) or cos (2.007128. . .). In this article, we will discuss the methods to find the value of cos 115 degrees with examples.

• Cos 115°: -0.4226182. . .
• Cos (-115 degrees): -0.4226182. . .
• Cos 115° in radians: cos (23π/36) or cos (2.0071286 . . .)

What is the Value of Cos 115 Degrees?

The value of cos 115 degrees in decimal is -0.422618261. . .. Cos 115 degrees can also be expressed using the equivalent of the given angle (115 degrees) in radians (2.00712 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 115 degrees = 115° × (π/180°) rad = 23π/36 or 2.0071 . . .
∴ cos 115° = cos(2.0071) = -0.4226182. . .

Explanation:

For cos 115 degrees, the angle 115° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 115° value = -0.4226182. . .
Since the cosine function is a periodic function, we can represent cos 115° as, cos 115 degrees = cos(115° + n × 360°), n ∈ Z.
⇒ cos 115° = cos 475° = cos 835°, and so on.
Note: Since, cosine is an even function, the value of cos(-115°) = cos(115°).

Methods to Find Value of Cos 115 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 115° is given as -0.42261. . .. We can find the value of cos 115 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 115 Degrees Using Unit Circle

To find the value of cos 115 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 115° angle with the positive x-axis.
• The cos of 115 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 115° = x = -0.4226 (approx)

Cos 115° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 115 degrees as:

• ± √(1-sin²(115°))
• ± 1/√(1 + tan²(115°))
• ± cot 115°/√(1 + cot²(115°))
• ±√(cosec²(115°) - 1)/cosec 115°
• 1/sec 115°

Note: Since 115° lies in the 2nd Quadrant, the final value of cos 115° will be negative.

We can use trigonometric identities to represent cos 115° as,

• -cos(180° - 115°) = -cos 65°
• -cos(180° + 115°) = -cos 295°
• sin(90° + 115°) = sin 205°
• sin(90° - 115°) = sin(-25°)

☛ Also Check:

• cos 36 degrees
• cos 1 degrees
• cos 120 degrees
• cos 570 degrees
• cos 780 degrees
• cos 69 degrees

FAQs on Cos 115 Degrees

What is Cos 115 Degrees?

Cos 115 degrees is the value of cosine trigonometric function for an angle equal to 115 degrees. The value of cos 115° is -0.4226 (approx)

What is the Value of Cos 115 Degrees in Terms of Tan 115°?

We know, using trig identities, we can write cos 115° as -1/√(1 + tan²(115°)). Here, the value of tan 115° is equal to -2.144506.

How to Find Cos 115° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 115° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(115°))
• ± 1/√(1 + tan²(115°))
• ± cot 115°/√(1 + cot²(115°))
• ± √(cosec²(115°) - 1)/cosec 115°
• 1/sec 115°

☛ Also check: trigonometric table

What is the Value of Cos 115° in Terms of Cosec 115°?

Since the cosine function can be represented using the cosecant function, we can write cos 115° as -[√(cosec²(115°) - 1)/cosec 115°]. The value of cosec 115° is equal to 1.10337.

How to Find the Value of Cos 115 Degrees?

The value of cos 115 degrees can be calculated by constructing an angle of 115° 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 115° is equal to the x-coordinate (-0.4226). ∴ cos 115° = -0.4226.