Cos 12 Degrees

The value of cos 12 degrees is 0.9781476. . .. Cos 12 degrees in radians is written as cos (12° × π/180°), i.e., cos (π/15) or cos (0.209439. . .). In this article, we will discuss the methods to find the value of cos 12 degrees with examples.

• Cos 12°: 0.9781476. . .
• Cos (-12 degrees): 0.9781476. . .
• Cos 12° in radians: cos (π/15) or cos (0.2094395 . . .)

What is the Value of Cos 12 Degrees?

The value of cos 12 degrees in decimal is 0.978147600. . .. Cos 12 degrees can also be expressed using the equivalent of the given angle (12 degrees) in radians (0.20943 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 12 degrees = 12° × (π/180°) rad = π/15 or 0.2094 . . .
∴ cos 12° = cos(0.2094) = 0.9781476. . .

Explanation:

For cos 12 degrees, the angle 12° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 12° value = 0.9781476. . .
Since the cosine function is a periodic function, we can represent cos 12° as, cos 12 degrees = cos(12° + n × 360°), n ∈ Z.
⇒ cos 12° = cos 372° = cos 732°, and so on.
Note: Since, cosine is an even function, the value of cos(-12°) = cos(12°).

Methods to Find Value of Cos 12 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 12° is given as 0.97814. . .. We can find the value of cos 12 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 12 Degrees Using Unit Circle

To find the value of cos 12 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 12° angle with the positive x-axis.
• The cos of 12 degrees equals the x-coordinate(0.9781) of the point of intersection (0.9781, 0.2079) of unit circle and r.

Hence the value of cos 12° = x = 0.9781 (approx)

Cos 12° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 12 degrees as:

• ± √(1-sin²(12°))
• ± 1/√(1 + tan²(12°))
• ± cot 12°/√(1 + cot²(12°))
• ±√(cosec²(12°) - 1)/cosec 12°
• 1/sec 12°

Note: Since 12° lies in the 1st Quadrant, the final value of cos 12° will be positive.

We can use trigonometric identities to represent cos 12° as,

• -cos(180° - 12°) = -cos 168°
• -cos(180° + 12°) = -cos 192°
• sin(90° + 12°) = sin 102°
• sin(90° - 12°) = sin 78°

☛ Also Check:

• cos 60 degrees
• cos 135 degrees
• cos 53 degrees
• cos 195 degrees
• cos 244 degrees
• cos 41 degrees

FAQs on Cos 12 Degrees

What is Cos 12 Degrees?

Cos 12 degrees is the value of cosine trigonometric function for an angle equal to 12 degrees. The value of cos 12° is 0.9781 (approx)

What is the Value of Cos 12 Degrees in Terms of Tan 12°?

We know, using trig identities, we can write cos 12° as 1/√(1 + tan²(12°)). Here, the value of tan 12° is equal to 0.212556.

How to Find Cos 12° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 12° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(12°))
• ± 1/√(1 + tan²(12°))
• ± cot 12°/√(1 + cot²(12°))
• ± √(cosec²(12°) - 1)/cosec 12°
• 1/sec 12°

☛ Also check: trigonometry table

What is the Value of Cos 12° in Terms of Sec 12°?

Since the secant function is the reciprocal of the cosine function, we can write cos 12° as 1/sec(12°). The value of sec 12° is equal to 1.022340.

How to Find the Value of Cos 12 Degrees?

The value of cos 12 degrees can be calculated by constructing an angle of 12° with the x-axis, and then finding the coordinates of the corresponding point (0.9781, 0.2079) on the unit circle. The value of cos 12° is equal to the x-coordinate (0.9781). ∴ cos 12° = 0.9781.