Cos 127 Degrees

The value of cos 127 degrees is -0.6018150. . .. Cos 127 degrees in radians is written as cos (127° × π/180°), i.e., cos (2.216568. . .). In this article, we will discuss the methods to find the value of cos 127 degrees with examples.

• Cos 127°: -0.6018150. . .
• Cos (-127 degrees): -0.6018150. . .
• Cos 127° in radians: cos (2.2165681 . . .)

What is the Value of Cos 127 Degrees?

The value of cos 127 degrees in decimal is -0.601815023. . .. Cos 127 degrees can also be expressed using the equivalent of the given angle (127 degrees) in radians (2.21656 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 127 degrees = 127° × (π/180°) rad = 2.2165 . . .
∴ cos 127° = cos(2.2165) = -0.6018150. . .

Explanation:

For cos 127 degrees, the angle 127° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 127° value = -0.6018150. . .
Since the cosine function is a periodic function, we can represent cos 127° as, cos 127 degrees = cos(127° + n × 360°), n ∈ Z.
⇒ cos 127° = cos 487° = cos 847°, and so on.
Note: Since, cosine is an even function, the value of cos(-127°) = cos(127°).

Methods to Find Value of Cos 127 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 127° is given as -0.60181. . .. We can find the value of cos 127 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 127 Degrees Using Unit Circle

To find the value of cos 127 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 127° angle with the positive x-axis.
• The cos of 127 degrees equals the x-coordinate(-0.6018) of the point of intersection (-0.6018, 0.7986) of unit circle and r.

Hence the value of cos 127° = x = -0.6018 (approx)

Cos 127° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 127 degrees as:

• ± √(1-sin²(127°))
• ± 1/√(1 + tan²(127°))
• ± cot 127°/√(1 + cot²(127°))
• ±√(cosec²(127°) - 1)/cosec 127°
• 1/sec 127°

Note: Since 127° lies in the 2nd Quadrant, the final value of cos 127° will be negative.

We can use trigonometric identities to represent cos 127° as,

• -cos(180° - 127°) = -cos 53°
• -cos(180° + 127°) = -cos 307°
• sin(90° + 127°) = sin 217°
• sin(90° - 127°) = sin(-37°)

☛ Also Check:

• cos 75 degrees
• cos 20 degrees
• cos 15 degrees
• cos 870 degrees
• cos 600 degrees
• cos 105 degrees

FAQs on Cos 127 Degrees

What is Cos 127 Degrees?

Cos 127 degrees is the value of cosine trigonometric function for an angle equal to 127 degrees. The value of cos 127° is -0.6018 (approx)

What is the Value of Cos 127° in Terms of Sec 127°?

Since the secant function is the reciprocal of the cosine function, we can write cos 127° as 1/sec(127°). The value of sec 127° is equal to -1.661640.

What is the Value of Cos 127 Degrees in Terms of Cot 127°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 127° can be written as cot 127°/√(1 + cot²(127°)). Here, the value of cot 127° is equal to -0.75355.

How to Find Cos 127° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 127° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(127°))
• ± 1/√(1 + tan²(127°))
• ± cot 127°/√(1 + cot²(127°))
• ± √(cosec²(127°) - 1)/cosec 127°
• 1/sec 127°

☛ Also check: trigonometric table

How to Find the Value of Cos 127 Degrees?

The value of cos 127 degrees can be calculated by constructing an angle of 127° with the x-axis, and then finding the coordinates of the corresponding point (-0.6018, 0.7986) on the unit circle. The value of cos 127° is equal to the x-coordinate (-0.6018). ∴ cos 127° = -0.6018.