Cos 106 Degrees

The value of cos 106 degrees is -0.2756373. . .. Cos 106 degrees in radians is written as cos (106° × π/180°), i.e., cos (53π/90) or cos (1.850049. . .). In this article, we will discuss the methods to find the value of cos 106 degrees with examples.

• Cos 106°: -0.2756373. . .
• Cos (-106 degrees): -0.2756373. . .
• Cos 106° in radians: cos (53π/90) or cos (1.8500490 . . .)

What is the Value of Cos 106 Degrees?

The value of cos 106 degrees in decimal is -0.275637355. . .. Cos 106 degrees can also be expressed using the equivalent of the given angle (106 degrees) in radians (1.85004 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 106 degrees = 106° × (π/180°) rad = 53π/90 or 1.8500 . . .
∴ cos 106° = cos(1.8500) = -0.2756373. . .

Explanation:

For cos 106 degrees, the angle 106° lies between 90° and 180° (Second Quadrant). Since cosine function is negative in the second quadrant, thus cos 106° value = -0.2756373. . .
Since the cosine function is a periodic function, we can represent cos 106° as, cos 106 degrees = cos(106° + n × 360°), n ∈ Z.
⇒ cos 106° = cos 466° = cos 826°, and so on.
Note: Since, cosine is an even function, the value of cos(-106°) = cos(106°).

Methods to Find Value of Cos 106 Degrees

The cosine function is negative in the 2nd quadrant. The value of cos 106° is given as -0.27563. . .. We can find the value of cos 106 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 106° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 106 degrees as:

• ± √(1-sin²(106°))
• ± 1/√(1 + tan²(106°))
• ± cot 106°/√(1 + cot²(106°))
• ±√(cosec²(106°) - 1)/cosec 106°
• 1/sec 106°

Note: Since 106° lies in the 2nd Quadrant, the final value of cos 106° will be negative.

We can use trigonometric identities to represent cos 106° as,

• -cos(180° - 106°) = -cos 74°
• -cos(180° + 106°) = -cos 286°
• sin(90° + 106°) = sin 196°
• sin(90° - 106°) = sin(-16°)

Cos 106 Degrees Using Unit Circle

To find the value of cos 106 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 106° angle with the positive x-axis.
• The cos of 106 degrees equals the x-coordinate(-0.2756) of the point of intersection (-0.2756, 0.9613) of unit circle and r.

Hence the value of cos 106° = x = -0.2756 (approx)

☛ Also Check:

• cos 20 degrees
• cos 36 degrees
• cos 3 degrees
• cos 59 degrees
• cos 600 degrees
• cos 47 degrees

FAQs on Cos 106 Degrees

What is Cos 106 Degrees?

Cos 106 degrees is the value of cosine trigonometric function for an angle equal to 106 degrees. The value of cos 106° is -0.2756 (approx)

How to Find Cos 106° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 106° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(106°))
• ± 1/√(1 + tan²(106°))
• ± cot 106°/√(1 + cot²(106°))
• ± √(cosec²(106°) - 1)/cosec 106°
• 1/sec 106°

☛ Also check: trigonometry table

How to Find the Value of Cos 106 Degrees?

The value of cos 106 degrees can be calculated by constructing an angle of 106° with the x-axis, and then finding the coordinates of the corresponding point (-0.2756, 0.9613) on the unit circle. The value of cos 106° is equal to the x-coordinate (-0.2756). ∴ cos 106° = -0.2756.

What is the Exact Value of cos 106 Degrees?

The exact value of cos 106 degrees can be given accurately up to 8 decimal places as -0.27563735.

What is the Value of Cos 106 Degrees in Terms of Sin 106°?

Using trigonometric identities, we can write cos 106° in terms of sin 106° as, cos(106°) = -√(1 - sin²(106°)). Here, the value of sin 106° is equal to 0.9613.