Cos 31 Degrees

The value of cos 31 degrees is 0.8571673. . .. Cos 31 degrees in radians is written as cos (31° × π/180°), i.e., cos (0.541052. . .). In this article, we will discuss the methods to find the value of cos 31 degrees with examples.

• Cos 31°: 0.8571673. . .
• Cos (-31 degrees): 0.8571673. . .
• Cos 31° in radians: cos (0.5410520 . . .)

What is the Value of Cos 31 Degrees?

The value of cos 31 degrees in decimal is 0.857167300. . .. Cos 31 degrees can also be expressed using the equivalent of the given angle (31 degrees) in radians (0.54105 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 31 degrees = 31° × (π/180°) rad = 0.5410 . . .
∴ cos 31° = cos(0.5410) = 0.8571673. . .

Explanation:

For cos 31 degrees, the angle 31° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 31° value = 0.8571673. . .
Since the cosine function is a periodic function, we can represent cos 31° as, cos 31 degrees = cos(31° + n × 360°), n ∈ Z.
⇒ cos 31° = cos 391° = cos 751°, and so on.
Note: Since, cosine is an even function, the value of cos(-31°) = cos(31°).

Methods to Find Value of Cos 31 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 31° is given as 0.85716. . .. We can find the value of cos 31 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 31 Degrees Using Unit Circle

To find the value of cos 31 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 31° angle with the positive x-axis.
• The cos of 31 degrees equals the x-coordinate(0.8572) of the point of intersection (0.8572, 0.515) of unit circle and r.

Hence the value of cos 31° = x = 0.8572 (approx)

Cos 31° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 31 degrees as:

• ± √(1-sin²(31°))
• ± 1/√(1 + tan²(31°))
• ± cot 31°/√(1 + cot²(31°))
• ±√(cosec²(31°) - 1)/cosec 31°
• 1/sec 31°

Note: Since 31° lies in the 1st Quadrant, the final value of cos 31° will be positive.

We can use trigonometric identities to represent cos 31° as,

• -cos(180° - 31°) = -cos 149°
• -cos(180° + 31°) = -cos 211°
• sin(90° + 31°) = sin 121°
• sin(90° - 31°) = sin 59°

☛ Also Check:

• cos 40 degrees
• cos 90 degrees
• cos 20 degrees
• cos 900 degrees
• cos 50 degrees
• cos 145 degrees

FAQs on Cos 31 Degrees

What is Cos 31 Degrees?

Cos 31 degrees is the value of cosine trigonometric function for an angle equal to 31 degrees. The value of cos 31° is 0.8572 (approx)

What is the Value of Cos 31° in Terms of Cosec 31°?

Since the cosine function can be represented using the cosecant function, we can write cos 31° as [√(cosec²(31°) - 1)/cosec 31°]. The value of cosec 31° is equal to 1.94160.

What is the Value of Cos 31 Degrees in Terms of Cot 31°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 31° can be written as cot 31°/√(1 + cot²(31°)). Here, the value of cot 31° is equal to 1.66427.

How to Find Cos 31° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 31° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(31°))
• ± 1/√(1 + tan²(31°))
• ± cot 31°/√(1 + cot²(31°))
• ± √(cosec²(31°) - 1)/cosec 31°
• 1/sec 31°

☛ Also check: trigonometric table

How to Find the Value of Cos 31 Degrees?

The value of cos 31 degrees can be calculated by constructing an angle of 31° with the x-axis, and then finding the coordinates of the corresponding point (0.8572, 0.515) on the unit circle. The value of cos 31° is equal to the x-coordinate (0.8572). ∴ cos 31° = 0.8572.