Tan 180 Degrees

The value of tan 180 degrees is 0. Tan 180 degrees in radians is written as tan (180° × π/180°), i.e., tan (π) or tan (3.141592. . .). In this article, we will discuss the methods to find the value of tan 180 degrees with examples.

• Tan 180°: 0
• Tan (-180 degrees): 0
• Tan 180° in radians: tan (π) or tan (3.1415926 . . .)

What is the Value of Tan 180 Degrees?

The value of tan 180 degrees is 0. Tan 180 degrees can also be expressed using the equivalent of the given angle (180 degrees) in radians (3.14159 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 180 degrees = 180° × (π/180°) rad = π or 3.1415 . . .
∴ tan 180° = tan(3.1415) = 0

Explanation:

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

Methods to Find Value of Tan 180 Degrees

The value of tan 180° is given as 0. We can find the value of tan 180 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 180° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 180 degrees as:

• sin(180°)/cos(180°)
• ± sin 180°/√(1 - sin²(180°))
• ± √(1 - cos²(180°))/cos 180°
• ± 1/√(cosec²(180°) - 1)
• ± √(sec²(180°) - 1)
• 1/cot 180°

Note: Since 180° lies on the negative x-axis, the final value of tan 180° is 0.

We can use trigonometric identities to represent tan 180° as,

• cot(90° - 180°) = cot(-90°)
• -cot(90° + 180°) = -cot 270°
• -tan (180° - 180°) = -tan 0°

Tan 180 Degrees Using Unit Circle

To find the value of tan 180 degrees using the unit circle:

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

☛ Also Check:

• tan 1 degrees
• tan 0 degrees
• tan 15 degrees
• tan 11 degrees
• tan 38 degrees
• tan 18 degrees

FAQs on Tan 180 Degrees

What is Tan 180 Degrees?

Tan 180 degrees is the value of tangent trigonometric function for an angle equal to 180 degrees. The value of tan 180° is 0.

How to Find the Value of Tan 180 Degrees?

The value of tan 180 degrees can be calculated by constructing an angle of 180° with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of tan 180° is equal to the y-coordinate(0) divided by the x-coordinate (-1). ∴ tan 180° = 0

What is the Value of Tan 180° in Terms of Sec 180°?

We can represent the tangent function in terms of the secant function using trig identities, tan 180° can be written as √(sec²(180°) - 1). Here, the value of sec 180° is equal to -1.

What is the Value of Tan 180 Degrees in Terms of Cot 180°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 180° as 1/cot(180°).

How to Find Tan 180° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 180° can be given in terms of other trigonometric functions as:

• sin(180°)/cos(180°)
• ± sin 180°/√(1 - sin²(180°))
• ± √(1 - cos²(180°))/cos 180°
• ± 1/√(cosec²(180°) - 1)
• ± √(sec²(180°) - 1)
• 1/cot 180°

☛ Also check: trigonometry table