Cos 56 Degrees

The value of cos 56 degrees is 0.5591929. . .. Cos 56 degrees in radians is written as cos (56° × π/180°), i.e., cos (14π/45) or cos (0.977384. . .). In this article, we will discuss the methods to find the value of cos 56 degrees with examples.

• Cos 56°: 0.5591929. . .
• Cos (-56 degrees): 0.5591929. . .
• Cos 56° in radians: cos (14π/45) or cos (0.9773843 . . .)

What is the Value of Cos 56 Degrees?

The value of cos 56 degrees in decimal is 0.559192903. . .. Cos 56 degrees can also be expressed using the equivalent of the given angle (56 degrees) in radians (0.97738 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 56 degrees = 56° × (π/180°) rad = 14π/45 or 0.9773 . . .
∴ cos 56° = cos(0.9773) = 0.5591929. . .

Explanation:

For cos 56 degrees, the angle 56° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 56° value = 0.5591929. . .
Since the cosine function is a periodic function, we can represent cos 56° as, cos 56 degrees = cos(56° + n × 360°), n ∈ Z.
⇒ cos 56° = cos 416° = cos 776°, and so on.
Note: Since, cosine is an even function, the value of cos(-56°) = cos(56°).

Methods to Find Value of Cos 56 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 56° is given as 0.55919. . .. We can find the value of cos 56 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 56 Degrees Using Unit Circle

To find the value of cos 56 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 56° angle with the positive x-axis.
• The cos of 56 degrees equals the x-coordinate(0.5592) of the point of intersection (0.5592, 0.829) of unit circle and r.

Hence the value of cos 56° = x = 0.5592 (approx)

Cos 56° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 56 degrees as:

• ± √(1-sin²(56°))
• ± 1/√(1 + tan²(56°))
• ± cot 56°/√(1 + cot²(56°))
• ±√(cosec²(56°) - 1)/cosec 56°
• 1/sec 56°

Note: Since 56° lies in the 1st Quadrant, the final value of cos 56° will be positive.

We can use trigonometric identities to represent cos 56° as,

• -cos(180° - 56°) = -cos 124°
• -cos(180° + 56°) = -cos 236°
• sin(90° + 56°) = sin 146°
• sin(90° - 56°) = sin 34°

☛ Also Check:

• cos 135 degrees
• cos 120 degrees
• cos 37 degrees
• cos 600 degrees
• cos 540 degrees
• cos 31 degrees

FAQs on Cos 56 Degrees

What is Cos 56 Degrees?

Cos 56 degrees is the value of cosine trigonometric function for an angle equal to 56 degrees. The value of cos 56° is 0.5592 (approx)

What is the Value of Cos 56 Degrees in Terms of Sin 56°?

Using trigonometric identities, we can write cos 56° in terms of sin 56° as, cos(56°) = √(1 - sin²(56°)). Here, the value of sin 56° is equal to 0.829.

What is the Value of Cos 56° in Terms of Cosec 56°?

Since the cosine function can be represented using the cosecant function, we can write cos 56° as [√(cosec²(56°) - 1)/cosec 56°]. The value of cosec 56° is equal to 1.20621.

How to Find the Value of Cos 56 Degrees?

The value of cos 56 degrees can be calculated by constructing an angle of 56° with the x-axis, and then finding the coordinates of the corresponding point (0.5592, 0.829) on the unit circle. The value of cos 56° is equal to the x-coordinate (0.5592). ∴ cos 56° = 0.5592.

How to Find Cos 56° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 56° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(56°))
• ± 1/√(1 + tan²(56°))
• ± cot 56°/√(1 + cot²(56°))
• ± √(cosec²(56°) - 1)/cosec 56°
• 1/sec 56°

☛ Also check: trigonometry table