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Tan 360 Degrees

The value of tan 360 degrees is 0. Tan 360 degrees in radians is written as tan (360° × π/180°), i.e., tan (2π) or tan (6.283185. . .). In this article, we will discuss the methods to find the value of tan 360 degrees with examples.

Tan 360°: 0
Tan (-360 degrees): 0
Tan 360° in radians: tan (2π) or tan (6.2831853 . . .)

What is the Value of Tan 360 Degrees?

The value of tan 360 degrees is 0. Tan 360 degrees can also be expressed using the equivalent of the given angle (360 degrees) in radians (6.28318 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 360 degrees = 360° × (π/180°) rad = 2π or 6.2831 . . .
∴ tan 360° = tan(6.2831) = 0

Explanation:

For tan 360 degrees, the angle 360° lies on the positive x-axis. Thus, tan 360° value = 0
Since the tangent function is a periodic function, we can represent tan 360° as, tan 360 degrees = tan(360° + n × 180°), n ∈ Z.
⇒ tan 360° = tan 540° = tan 720°, and so on.
Note: Since, tangent is an odd function, the value of tan(-360°) = -tan(360°) = 0.

Methods to Find Value of Tan 360 Degrees

The value of tan 360° is given as 0. We can find the value of tan 360 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 360 Degrees Using Unit Circle

To find the value of tan 360 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 0° or 360° angle with the positive x-axis.
The tan of 360 degrees equals the y-coordinate(0) divided by x-coordinate(1) of the point of intersection (1, 0) of unit circle and r.

Hence the value of tan 360° = y/x = 0

Tan 360° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 360 degrees as:

sin(360°)/cos(360°)
± sin 360°/√(1 - sin²(360°))
± √(1 - cos²(360°))/cos 360°
± 1/√(cosec²(360°) - 1)
± √(sec²(360°) - 1)
1/cot 360°

We can use trigonometric identities to represent tan 360° as,

cot(90° - 360°) = cot(-270°)
-cot(90° + 360°) = -cot 450°
-tan (180° - 360°) = -tan(-180°)

Note: Since 360° lies on the positive x-axis, the final value of tan 360° is 0.

☛ Also Check:

Examples Using Tan 360 Degrees

Example 1: Find the value of 4 tan(360°)/6 tan(45°).

Solution:

Using trigonometric values, we know, tan(360°) = 0 and tan 45° = 1.
⇒ Value of 4 tan(360°)/6 tan(45°) = 0
Example 2: Simplify: 6 (tan 360°/cot(225°))

Solution:

We know tan 360° = 0 and cot 225° = 1
⇒ 6 tan 360°/cot 225° = 6(0)
= 0
Example 3: Find the value of (2 sin (180°) cos (180°) sec (360°)). [Hint: Use tan 360° = 0]

Solution:

Using sin 2a formula,
2 sin (180°) cos (180°) = sin (2 × 180°) = sin 360°
⇒ 2 sin (180°) cos (180°) sec(360°) = sin 360° sec 360°
= sin 360°/cos 360° = tan 360°
⇒ (2 sin (180°) cos (180°) sec(360°)) = 0

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FAQs on Tan 360 Degrees

What is Tan 360 Degrees?

Tan 360 degrees is the value of tangent trigonometric function for an angle equal to 360 degrees. The value of tan 360° is 0.

What is the Value of Tan 360° in Terms of Sec 360°?

We can represent the tangent function in terms of the secant function using trig identities, tan 360° can be written as √(sec²(360°) - 1). Here, the value of sec 360° is equal to 1.

What is the Value of Tan 360 Degrees in Terms of Cot 360°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 360° as 1/cot(360°).

How to Find the Value of Tan 360 Degrees?

The value of tan 360 degrees can be calculated by constructing an angle of 360° with the x-axis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of tan 360° is equal to the y-coordinate(0) divided by the x-coordinate (1). ∴ tan 360° = 0

How to Find Tan 360° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 360° can be given in terms of other trigonometric functions as:

sin(360°)/cos(360°)
± sin 360°/√(1 - sin²(360°))
± √(1 - cos²(360°))/cos 360°
± 1/√(cosec²(360°) - 1)
± √(sec²(360°) - 1)
1/cot 360°

☛ Also check: trigonometry table

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