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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 yaxis. 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 xaxis.
 The tan of 270 degrees equals the ycoordinate(1) divided by xcoordinate(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 yaxis, the final value of tan 270° is not defined.
☛ Also Check:
Examples Using Tan 270 Degrees

Example 1: Find the value of tan 270° using the value of cos 270° and sin 270°.
Solution:
We know, tan 270° = sin 270°/cos 270°
= 1/0
= not defined 
Example 2: Simplify: (tan 270°/cot 45°)
Solution:
We know tan 270° = not defined and cot 45° = 1
⇒ tan 270°/cot 45° = not defined 
Example 3: Find the value of (2 sin (135°) cos (135°) sec (270°)).
Solution:
Using sin 2a formula,
2 sin (135°) cos (135°) = sin (2 × 135°) = sin 270°
⇒ 2 sin (135°) cos (135°) sec(270°) = sin 270° sec 270°
= sin 270°/cos 270° = tan 270°
⇒ (2 sin (135°) cos (135°) sec(270°)) = not defined
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 xaxis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of tan 270° is equal to the ycoordinate(1) divided by the xcoordinate (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.
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