Cos 27 Degrees

The value of cos 27 degrees is 0.8910065. . .. Cos 27 degrees in radians is written as cos (27° × π/180°), i.e., cos (3π/20) or cos (0.471238. . .). In this article, we will discuss the methods to find the value of cos 27 degrees with examples.

• Cos 27°: 0.8910065. . .
• Cos (-27 degrees): 0.8910065. . .
• Cos 27° in radians: cos (3π/20) or cos (0.4712388 . . .)

What is the Value of Cos 27 Degrees?

The value of cos 27 degrees in decimal is 0.891006524. . .. Cos 27 degrees can also be expressed using the equivalent of the given angle (27 degrees) in radians (0.47123 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 27 degrees = 27° × (π/180°) rad = 3π/20 or 0.4712 . . .
∴ cos 27° = cos(0.4712) = 0.8910065. . .

Explanation:

For cos 27 degrees, the angle 27° lies between 0° and 90° (First Quadrant). Since cosine function is positive in the first quadrant, thus cos 27° value = 0.8910065. . .
Since the cosine function is a periodic function, we can represent cos 27° as, cos 27 degrees = cos(27° + n × 360°), n ∈ Z.
⇒ cos 27° = cos 387° = cos 747°, and so on.
Note: Since, cosine is an even function, the value of cos(-27°) = cos(27°).

Methods to Find Value of Cos 27 Degrees

The cosine function is positive in the 1st quadrant. The value of cos 27° is given as 0.89100. . .. We can find the value of cos 27 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Cos 27 Degrees Using Unit Circle

To find the value of cos 27 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 27° angle with the positive x-axis.
• The cos of 27 degrees equals the x-coordinate(0.891) of the point of intersection (0.891, 0.454) of unit circle and r.

Hence the value of cos 27° = x = 0.891 (approx)

Cos 27° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the cos 27 degrees as:

• ± √(1-sin²(27°))
• ± 1/√(1 + tan²(27°))
• ± cot 27°/√(1 + cot²(27°))
• ±√(cosec²(27°) - 1)/cosec 27°
• 1/sec 27°

Note: Since 27° lies in the 1st Quadrant, the final value of cos 27° will be positive.

We can use trigonometric identities to represent cos 27° as,

• -cos(180° - 27°) = -cos 153°
• -cos(180° + 27°) = -cos 207°
• sin(90° + 27°) = sin 117°
• sin(90° - 27°) = sin 63°

☛ Also Check:

• cos 360 degrees
• cos 11 degrees
• cos 135 degrees
• cos 285 degrees
• cos 160 degrees
• cos 250 degrees

FAQs on Cos 27 Degrees

What is Cos 27 Degrees?

Cos 27 degrees is the value of cosine trigonometric function for an angle equal to 27 degrees. The value of cos 27° is 0.891 (approx)

What is the Value of Cos 27° in Terms of Sec 27°?

Since the secant function is the reciprocal of the cosine function, we can write cos 27° as 1/sec(27°). The value of sec 27° is equal to 1.122326.

What is the Value of Cos 27 Degrees in Terms of Cot 27°?

We can represent the cosine function in terms of the cotangent function using trig identities, cos 27° can be written as cot 27°/√(1 + cot²(27°)). Here, the value of cot 27° is equal to 1.96261.

How to Find the Value of Cos 27 Degrees?

The value of cos 27 degrees can be calculated by constructing an angle of 27° with the x-axis, and then finding the coordinates of the corresponding point (0.891, 0.454) on the unit circle. The value of cos 27° is equal to the x-coordinate (0.891). ∴ cos 27° = 0.891.

How to Find Cos 27° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cos 27° can be given in terms of other trigonometric functions as:

• ± √(1-sin²(27°))
• ± 1/√(1 + tan²(27°))
• ± cot 27°/√(1 + cot²(27°))
• ± √(cosec²(27°) - 1)/cosec 27°
• 1/sec 27°

☛ Also check: trigonometry table