Tan 720 Degrees

The value of tan 720 degrees is 0. Tan 720 degrees in radians is written as tan (720° × π/180°), i.e., tan (4π) or tan (12.566370. . .). In this article, we will discuss the methods to find the value of tan 720 degrees with examples.

• Tan 720°: 0
• Tan (-720 degrees): 0
• Tan 720° in radians: tan (4π) or tan (12.5663706 . . .)

What is the Value of Tan 720 Degrees?

The value of tan 720 degrees is 0. Tan 720 degrees can also be expressed using the equivalent of the given angle (720 degrees) in radians (12.56637 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 720 degrees = 720° × (π/180°) rad = 4π or 12.5663 . . .
∴ tan 720° = tan(12.5663) = 0

Explanation:

For tan 720°, the angle 720° > 360°. We can represent tan 720° as, tan(720° mod 360°) = tan(0°). The angle 720°, coterminal to angle 0°, lies on the positive x-axis.
Thus tan 720 degrees value = 0
Similarly, given the periodic property of tan 720°, it can also be written as, tan 720 degrees = (720° + n × 180°), n ∈ Z.
⇒ tan 720° = tan 900° = tan 1080°, and so on.
Note: Since, tangent is an odd function, the value of tan(-720°) = -tan(720°) = 0.

Methods to Find Value of Tan 720 Degrees

The value of tan 720° is given as 0. We can find the value of tan 720 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Tan 720 Degrees Using Unit Circle

To find the value of tan 720 degrees using the unit circle, represent 720° in the form (2 × 360°) + 0° [∵ 720°>360°] ∵ The angle 720° is coterminal to 0° angle and also tangent is a periodic function, tan 720° = tan 0°.

• Rotate ‘r’ anticlockwise to form 0° or 720° angle with the positive x-axis.
• The tan of 720 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 720° = y/x = 0

Tan 720° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 720 degrees as:

• sin(720°)/cos(720°)
• ± sin 720°/√(1 - sin²(720°))
• ± √(1 - cos²(720°))/cos 720°
• ± 1/√(cosec²(720°) - 1)
• ± √(sec²(720°) - 1)
• 1/cot 720°

Note: Since 720° lies on the positive x-axis, the final value of tan 720° is 0.

We can use trigonometric identities to represent tan 720° as,

• cot(90° - 720°) = cot(-630°)
• -cot(90° + 720°) = -cot 810°
• -tan (180° - 720°) = -tan(-540°)

☛ Also Check:

• tan 180 degrees
• tan 40 degrees
• tan 60 degrees
• tan 1260 degrees
• tan 165 degrees
• tan 42 degrees

FAQs on Tan 720 Degrees

What is Tan 720 Degrees?

Tan 720 degrees is the value of tangent trigonometric function for an angle equal to 720 degrees. The value of tan 720° is 0.

What is the Exact Value of tan 720 Degrees?

The exact value of tan 720 degrees is 0.

How to Find Tan 720° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 720° can be given in terms of other trigonometric functions as:

• sin(720°)/cos(720°)
• ± sin 720°/√(1 - sin²(720°))
• ± √(1 - cos²(720°))/cos 720°
• ± 1/√(cosec²(720°) - 1)
• ± √(sec²(720°) - 1)
• 1/cot 720°

☛ Also check: trigonometric table

How to Find the Value of Tan 720 Degrees?

The value of tan 720 degrees can be calculated by constructing an angle of 720° with the x-axis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of tan 720° is equal to the y-coordinate(0) divided by the x-coordinate (1). ∴ tan 720° = 0

What is the Value of Tan 720 Degrees in Terms of Sin 720°?

Using trigonometric identities, we can write tan 720° in terms of sin 720° as, tan(720°) = sin 720°/√(1 - sin²(720°)) . Here, the value of sin 720° is equal to 0.