Tan 27 Degrees

The value of tan 27 degrees is 0.5095254. . .. Tan 27 degrees in radians is written as tan (27° × π/180°), i.e., tan (3π/20) or tan (0.471238. . .). In this article, we will discuss the methods to find the value of tan 27 degrees with examples.

• Tan 27° in decimal: 0.5095254. . .
• Tan (-27 degrees): -0.5095254. . .
• Tan 27° in radians: tan (3π/20) or tan (0.4712388 . . .)

What is the Value of Tan 27 Degrees?

The value of tan 27 degrees in decimal is 0.509525449. . .. Tan 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 . . .
∴ tan 27° = tan(0.4712) = 0.5095254. . .

Explanation:

For tan 27 degrees, the angle 27° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 27° value = 0.5095254. . .
Since the tangent function is a periodic function, we can represent tan 27° as, tan 27 degrees = tan(27° + n × 180°), n ∈ Z.
⇒ tan 27° = tan 207° = tan 387°, and so on.
Note: Since, tangent is an odd function, the value of tan(-27°) = -tan(27°).

Methods to Find Value of Tan 27 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 27° is given as 0.50952. . .. We can find the value of tan 27 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 27 Degrees Using Unit Circle

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

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

Hence the value of tan 27° = y/x = 0.5095 (approx).

Tan 27° in Terms of Trigonometric Functions

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

• sin(27°)/cos(27°)
• ± sin 27°/√(1 - sin²(27°))
• ± √(1 - cos²(27°))/cos 27°
• ± 1/√(cosec²(27°) - 1)
• ± √(sec²(27°) - 1)
• 1/cot 27°

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

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

• cot(90° - 27°) = cot 63°
• -cot(90° + 27°) = -cot 117°
• -tan (180° - 27°) = -tan 153°

☛ Also Check:

• tan 225 degrees
• tan 135 degrees
• tan 150 degrees
• tan 195 degrees
• tan 4 degrees
• tan 23 degrees

FAQs on Tan 27 Degrees

What is Tan 27 Degrees?

Tan 27 degrees is the value of tangent trigonometric function for an angle equal to 27 degrees. The value of tan 27° is 0.5095 (approx).

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

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

• sin(27°)/cos(27°)
• ± sin 27°/√(1 - sin²(27°))
• ± √(1 - cos²(27°))/cos 27°
• ± 1/√(cosec²(27°) - 1)
• ± √(sec²(27°) - 1)
• 1/cot 27°

☛ Also check: trigonometry table

How to Find the Value of Tan 27 Degrees?

The value of tan 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 tan 27° is equal to the y-coordinate(0.454) divided by the x-coordinate (0.891). ∴ tan 27° = 0.5095

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

We can represent the tangent function in terms of the secant function using trig identities, tan 27° can be written as √(sec²(27°) - 1). Here, the value of sec 27° is equal to 1.1223.

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

Since the tangent function is the reciprocal of the cotangent function, we can write tan 27° as 1/cot(27°). The value of cot 27° is equal to 1.96261.