Tan 270 Degrees

The value of tan 270 degrees is undefined. Tan 270 degrees in radians is written as tan (270° × π/180°), i.e., tan (3π/2) or tan (4.712388. . .). In this article, we will discuss the methods to find the value of tan 270 degrees with examples.

• Tan 270°: undefined
• Tan (-270 degrees): undefined
• Tan 270° in radians: tan (3π/2) or tan (4.7123889 . . .)

What is the Value of Tan 270 Degrees?

The value of tan 270 degrees is undefined. Tan 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123 . . .
∴ tan 270° = tan(4.7123) = undefined

Explanation:

For tan 270 degrees, the angle 270° lies on the negative y-axis. Thus tan 270° value is not defined.
Since the tangent function is a periodic function, we can represent tan 270° as, tan 270 degrees = tan(270° + n × 180°), n ∈ Z.
⇒ tan 270° = tan 450° = tan 630°, and so on.
Note: Since, tangent is an odd function, the value of tan(-270°) = -tan(270°) = undefined.

Methods to Find Value of Tan 270 Degrees

The value of tan 270° is given as not defined. We can find the value of tan 270 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 270 Degrees Using Unit Circle

To find the value of tan 270 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 270° angle with the positive x-axis.
• The tan of 270 degrees equals the y-coordinate(-1) divided by x-coordinate(0) of the point of intersection (0, -1) of unit circle and r.

Hence the value of tan 270° = not defined.

Tan 270° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 270 degrees as:

• sin(270°)/cos(270°)
• ± sin 270°/√(1 - sin²(270°))
• ± √(1 - cos²(270°))/cos 270°
• ± 1/√(cosec²(270°) - 1)
• ± √(sec²(270°) - 1)
• 1/cot 270°

We can use trigonometric identities to represent tan 270° as,

• cot(90° - 270°) = cot(-180°)
• -cot(90° + 270°) = -cot 360°
• -tan (180° - 270°) = -tan(-90°)

Note: Since 270° lies on the negative y-axis, the final value of tan 270° is not defined.

☛ Also Check:

• tan 45 degrees
• tan 2 degrees
• tan 1 degrees
• tan 255 degrees
• tan 100 degrees
• tan 405 degrees

FAQs on Tan 270 Degrees

What is Tan 270 Degrees?

Tan 270 degrees is the value of tangent trigonometric function for an angle equal to 270 degrees. The value of tan 270° is not defined.

How to Find Tan 270° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 270° can be given in terms of other trigonometric functions as:

• sin(270°)/cos(270°)
• ± sin 270°/√(1 - sin²(270°))
• ± √(1 - cos²(270°))/cos 270°
• ± 1/√(cosec²(270°) - 1)
• ± √(sec²(270°) - 1)
• 1/cot 270°

☛ Also check: trigonometric table

What is the Exact Value of tan 270 Degrees?

The exact value of tan 270 degrees is not defined.

How to Find the Value of Tan 270 Degrees?

The value of tan 270 degrees can be calculated by constructing an angle of 270° with the x-axis, and then finding the coordinates of the corresponding point (0, -1) on the unit circle. The value of tan 270° is equal to the y-coordinate(-1) divided by the x-coordinate (0). ∴ tan 270° = not defined

What is the Value of Tan 270 Degrees in Terms of Cot 270°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 270° as 1/cot(270°). The value of cot 270° is equal to 0.