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Tan 255 Degrees

The value of tan 255 degrees is 3.7320508. . .. Tan 255 degrees in radians is written as tan (255° × π/180°), i.e., tan (17π/12) or tan (4.450589. . .). In this article, we will discuss the methods to find the value of tan 255 degrees with examples.

Tan 255°: 2 + √3
Tan 255° in decimal: 3.7320508. . .
Tan (-255 degrees): -3.7320508. . . or -2 - √3
Tan 255° in radians: tan (17π/12) or tan (4.4505895 . . .)

What is the Value of Tan 255 Degrees?

The value of tan 255 degrees in decimal is 3.732050807. . .. Tan 255 degrees can also be expressed using the equivalent of the given angle (255 degrees) in radians (4.45058 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 255 degrees = 255° × (π/180°) rad = 17π/12 or 4.4505 . . .
∴ tan 255° = tan(4.4505) = 2 + √3 or 3.7320508. . .

Explanation:

For tan 255 degrees, the angle 255° lies between 180° and 270° (Third Quadrant). Since tangent function is positive in the third quadrant, thus tan 255° value = 2 + √3 or 3.7320508. . .
Since the tangent function is a periodic function, we can represent tan 255° as, tan 255 degrees = tan(255° + n × 180°), n ∈ Z.
⇒ tan 255° = tan 435° = tan 615°, and so on.
Note: Since, tangent is an odd function, the value of tan(-255°) = -tan(255°).

Methods to Find Value of Tan 255 Degrees

The tangent function is positive in the 3rd quadrant. The value of tan 255° is given as 3.73205. . .. We can find the value of tan 255 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 255 Degrees Using Unit Circle

To find the value of tan 255 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 255° angle with the positive x-axis.
The tan of 255 degrees equals the y-coordinate(-0.9659) divided by x-coordinate(-0.2588) of the point of intersection (-0.2588, -0.9659) of unit circle and r.

Hence the value of tan 255° = y/x = 3.7321 (approx).

Tan 255° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 255 degrees as:

sin(255°)/cos(255°)
± sin 255°/√(1 - sin²(255°))
± √(1 - cos²(255°))/cos 255°
± 1/√(cosec²(255°) - 1)
± √(sec²(255°) - 1)
1/cot 255°

Note: Since 255° lies in the 3rd Quadrant, the final value of tan 255° will be positive.

We can use trigonometric identities to represent tan 255° as,

cot(90° - 255°) = cot(-165°)
-cot(90° + 255°) = -cot 345°
-tan (180° - 255°) = -tan(-75°)

☛ Also Check:

Examples Using Tan 255 Degrees

Example 1: Find the value of tan 255° if cot 255° is 0.2679.

Solution:
Since, tan 255° = 1/cot 255°
⇒ tan 255° = 1/0.2679 = 3.7321
Example 2: Using the value of tan 255°, solve: (sec²(255°) - 1).

Solution:
We know, (sec²(255°) - 1) = (tan²(255°)) = 13.9282
⇒ (sec²(255°) - 1) = 13.9282
Example 3: Find the value of (2 sin (127.5°) cos (127.5°) sec (255°)). [Hint: Use tan 255° = 3.7321]

Solution:

Using sin 2a formula,
2 sin (127.5°) cos (127.5°) = sin (2 × 127.5°) = sin 255°
⇒ 2 sin (127.5°) cos (127.5°) sec(255°) = sin 255° sec 255°
= sin 255°/cos 255° = tan 255°
⇒ (2 sin (127.5°) cos (127.5°) sec(255°)) = 3.7321

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FAQs on Tan 255 Degrees

What is Tan 255 Degrees?

Tan 255 degrees is the value of tangent trigonometric function for an angle equal to 255 degrees. The value of tan 255° is 2 + √3 or 3.7321 (approx).

What is the Value of Tan 255° in Terms of Cosec 255°?

Since the tangent function can be represented using the cosecant function, we can write tan 255° as 1/√(cosec²(255°) - 1). The value of cosec 255° is equal to -1.03527.

How to Find Tan 255° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 255° can be given in terms of other trigonometric functions as:

sin(255°)/cos(255°)
± sin 255°/√(1 - sin²(255°))
± √(1 - cos²(255°))/cos 255°
± 1/√(cosec²(255°) - 1)
± √(sec²(255°) - 1)
1/cot 255°

☛ Also check: trigonometry table

What is the Value of Tan 255 Degrees in Terms of Cot 255°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 255° as 1/cot(255°). The value of cot 255° is equal to 2 - √3.

How to Find the Value of Tan 255 Degrees?

The value of tan 255 degrees can be calculated by constructing an angle of 255° with the x-axis, and then finding the coordinates of the corresponding point (-0.2588, -0.9659) on the unit circle. The value of tan 255° is equal to the y-coordinate(-0.9659) divided by the x-coordinate (-0.2588). ∴ tan 255° = 2 + √3 or 3.7321

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