Tan 540 Degrees

The value of tan 540 degrees is 0. Tan 540 degrees in radians is written as tan (540° × π/180°), i.e., tan (3π) or tan (9.424777. . .). In this article, we will discuss the methods to find the value of tan 540 degrees with examples.

• Tan 540°: 0
• Tan (-540 degrees): 0
• Tan 540° in radians: tan (3π) or tan (9.4247779 . . .)

What is the Value of Tan 540 Degrees?

The value of tan 540 degrees is 0. Tan 540 degrees can also be expressed using the equivalent of the given angle (540 degrees) in radians (9.42477 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 540 degrees = 540° × (π/180°) rad = 3π or 9.4247 . . .
∴ tan 540° = tan(9.4247) = 0

Explanation:

For tan 540°, the angle 540° > 360°. We can represent tan 540° as, tan(540° mod 360°) = tan(180°). The angle 540°, coterminal to angle 180°, lies on the negative x-axis.
Thus, tan 540 degrees value = 0
Similarly, given the periodic property of tan 540°, it can also be written as, tan 540 degrees = (540° + n × 180°), n ∈ Z.
⇒ tan 540° = tan 720° = tan 900°, and so on.
Note: Since, tangent is an odd function, the value of tan(-540°) = -tan(540°) = 0.

Methods to Find Value of Tan 540 Degrees

The value of tan 540° is given as 0. We can find the value of tan 540 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 540° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 540 degrees as:

• sin(540°)/cos(540°)
• ± sin 540°/√(1 - sin²(540°))
• ± √(1 - cos²(540°))/cos 540°
• ± 1/√(cosec²(540°) - 1)
• ± √(sec²(540°) - 1)
• 1/cot 540°

Note: Since 540° lies on the negative x-axis, the final value of tan 540° is 0.

We can use trigonometric identities to represent tan 540° as,

• cot(90° - 540°) = cot(-450°)
• -cot(90° + 540°) = -cot 630°
• -tan (180° - 540°) = -tan(-360°)

Tan 540 Degrees Using Unit Circle

To find the value of tan 540 degrees using the unit circle, represent 540° in the form (1 × 360°) + 180° [∵ 540°>360°] ∵ The angle 540° is coterminal to 180° angle and also tangent is a periodic function, tan 540° = tan 180°.

• Rotate ‘r’ anticlockwise to form 180° or 540° angle with the positive x-axis.
• The tan of 540 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 540° = y/x = 0

☛ Also Check:

• tan 15 degrees
• tan 20 degrees
• tan 45 degrees
• tan 8 degrees
• tan 130 degrees
• tan 73 degrees

FAQs on Tan 540 Degrees

What is Tan 540 Degrees?

Tan 540 degrees is the value of tangent trigonometric function for an angle equal to 540 degrees. The value of tan 540° is 0.

What is the Value of Tan 540° in Terms of Sec 540°?

We can represent the tangent function in terms of the secant function using trig identities, tan 540° can be written as √(sec²(540°) - 1). Here, the value of sec 540° is equal to -1.

How to Find Tan 540° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 540° can be given in terms of other trigonometric functions as:

• sin(540°)/cos(540°)
• ± sin 540°/√(1 - sin²(540°))
• ± √(1 - cos²(540°))/cos 540°
• ± 1/√(cosec²(540°) - 1)
• ± √(sec²(540°) - 1)
• 1/cot 540°

☛ Also check: trigonometry table

How to Find the Value of Tan 540 Degrees?

The value of tan 540 degrees can be calculated by constructing an angle of 540° with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of tan 540° is equal to the y-coordinate(0) divided by the x-coordinate (-1). ∴ tan 540° = 0

What is the Value of Tan 540 Degrees in Terms of Cot 540°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 540° as 1/cot(540°).