Cos 126 Degrees

The value of cos 126 degrees is -0.5877852. . .. Cos 126 degrees in radians is written as cos (126° × π/180°), i.e., cos (7π/10) or cos (2.199114. . .). In this article, we will discuss the methods to find the value of cos 126 degrees with examples.

• Cos 126°: -0.5877852. . .
• Cos 126° in fraction: -√(10 - 2√5)/4
• Cos (-126 degrees): -0.5877852. . .
• Cos 126° in radians: cos (7π/10) or cos (2.1991148 . . .)

What is the Value of Cos 126 Degrees?

The value of cos 126 degrees in decimal is -0.587785252. . .. Cos 126 degrees can also be expressed using the equivalent of the given angle (126 degrees) in radians (2.19911 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 126 degrees = 126° × (π/180°) rad = 7π/10 or 2.1991 . . .
∴ cos 126° = cos(2.1991) = -√(10 - 2√5)/4 or -0.5877852. . .

Explanation:

For cos 126 degrees, the angle 126° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 126° value = -√(10 - 2√5)/4 or -0.5877852. . .
Since the cosine function is a periodic function, we can represent cos 126° as, cos 126 degrees = cos(126° + n × 360°), n ∈ Z.
⇒ cos 126° = cos 486° = cos 846°, and so on.
Note: Since, cosine is an even function, the value of cos(-126°) = cos(126°).

Methods to Find Value of Cos 126 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 126° is given as -0.58778. . .. We can find the value of cos 126 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 126° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 126 degrees as:

• ± √(1-sin²(126°))
• ± 1/√(1 + tan²(126°))
• ± cot 126°/√(1 + cot²(126°))
• ±√(cosec²(126°) - 1)/cosec 126°
• 1/sec 126°

Note: Since 126° lies in the 2nd Quadrant, the final value of cos 126° will be negative.

We can use trigonometric identities to represent cos 126° as,

• -cos(180° - 126°) = -cos 54°
• -cos(180° + 126°) = -cos 306°
• sin(90° + 126°) = sin 216°
• sin(90° - 126°) = sin(-36°)

Cos 126 Degrees Using Unit Circle

To find the value of cos 126 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 126° angle with the positive x-axis.
• The cos of 126 degrees equals the x-coordinate(-0.5878) of the point of intersection (-0.5878, 0.809) of unit circle and r.

Hence the value of cos 126° = x = -0.5878 (approx)

☛ Also Check:

• cos 360 degrees
• cos 40 degrees
• cos 135 degrees
• cos 14 degrees
• cos 870 degrees
• cos 13 degrees

FAQs on Cos 126 Degrees

What is Cos 126 Degrees?

Cos 126 degrees is the value of cosine trigonometric function for an angle equal to 126 degrees. The value of cos 126° is -√(10 - 2√5)/4 or -0.5878 (approx)

What is the Value of Cos 126 Degrees in Terms of Tan 126°?

We know, using trig identities, we can write cos 126° as -1/√(1 + tan²(126°)). Here, the value of tan 126° is equal to -1.376381.

What is the Value of Cos 126° in Terms of Sec 126°?

Since the secant function is the reciprocal of the cosine function, we can write cos 126° as 1/sec(126°). The value of sec 126° is equal to -1.701301.

How to Find Cos 126° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 126° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(126°))
• ± 1/√(1 + tan²(126°))
• ± cot 126°/√(1 + cot²(126°))
• ± √(cosec²(126°) - 1)/cosec 126°
• 1/sec 126°

☛ Also check: trigonometry table

How to Find the Value of Cos 126 Degrees?

The value of cos 126 degrees can be calculated by constructing an angle of 126° with the x-axis, and then finding the coordinates of the corresponding point (-0.5878, 0.809) on the unit circle. The value of cos 126° is equal to the x-coordinate (-0.5878). ∴ cos 126° = -0.5878.