Cos 14 Degrees

The value of cos 14 degrees is 0.9702957. . .. Cos 14 degrees in radians is written as cos (14° × π/180°), i.e., cos (7π/90) or cos (0.244346. . .). In this article, we will discuss the methods to find the value of cos 14 degrees with examples.

• Cos 14°: 0.9702957. . .
• Cos (-14 degrees): 0.9702957. . .
• Cos 14° in radians: cos (7π/90) or cos (0.2443460 . . .)

What is the Value of Cos 14 Degrees?

The value of cos 14 degrees in decimal is 0.970295726. . .. Cos 14 degrees can also be expressed using the equivalent of the given angle (14 degrees) in radians (0.24434 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 14 degrees = 14° × (π/180°) rad = 7π/90 or 0.2443 . . .
∴ cos 14° = cos(0.2443) = 0.9702957. . .

Explanation:

For cos 14 degrees, the angle 14° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 14° value = 0.9702957. . .
Since the cosine function is a periodic function, we can represent cos 14° as, cos 14 degrees = cos(14° + n × 360°), n ∈ Z.
⇒ cos 14° = cos 374° = cos 734°, and so on.
Note: Since, cosine is an even function, the value of cos(-14°) = cos(14°).

Methods to Find Value of Cos 14 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 14° is given as 0.97029. . .. We can find the value of cos 14 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Cos 14° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 14 degrees as:

• ± √(1-sin²(14°))
• ± 1/√(1 + tan²(14°))
• ± cot 14°/√(1 + cot²(14°))
• ±√(cosec²(14°) - 1)/cosec 14°
• 1/sec 14°

Note: Since 14° lies in the 1st Quadrant, the final value of cos 14° will be positive.

We can use trigonometric identities to represent cos 14° as,

• -cos(180° - 14°) = -cos 166°
• -cos(180° + 14°) = -cos 194°
• sin(90° + 14°) = sin 104°
• sin(90° - 14°) = sin 76°

Cos 14 Degrees Using Unit Circle

To find the value of cos 14 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 14° angle with the positive x-axis.
• The cos of 14 degrees equals the x-coordinate(0.9703) of the point of intersection (0.9703, 0.2419) of unit circle and r.

Hence the value of cos 14° = x = 0.9703 (approx)

☛ Also Check:

• cos 90 degrees
• cos 10 degrees
• cos 40 degrees
• cos 765 degrees
• cos 108 degrees
• cos 49 degrees

FAQs on Cos 14 Degrees

What is Cos 14 Degrees?

Cos 14 degrees is the value of cosine trigonometric function for an angle equal to 14 degrees. The value of cos 14° is 0.9703 (approx)

How to Find the Value of Cos 14 Degrees?

The value of cos 14 degrees can be calculated by constructing an angle of 14° with the x-axis, and then finding the coordinates of the corresponding point (0.9703, 0.2419) on the unit circle. The value of cos 14° is equal to the x-coordinate (0.9703). ∴ cos 14° = 0.9703.

What is the Value of Cos 14° in Terms of Sec 14°?

Since the secant function is the reciprocal of the cosine function, we can write cos 14° as 1/sec(14°). The value of sec 14° is equal to 1.030613.

How to Find Cos 14° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 14° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(14°))
• ± 1/√(1 + tan²(14°))
• ± cot 14°/√(1 + cot²(14°))
• ± √(cosec²(14°) - 1)/cosec 14°
• 1/sec 14°

☛ Also check: trigonometry table

What is the Value of Cos 14 Degrees in Terms of Sin 14°?

Using trigonometric identities, we can write cos 14° in terms of sin 14° as, cos(14°) = √(1 - sin²(14°)). Here, the value of sin 14° is equal to 0.2419.