Tan 0 Degrees

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

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

What is the Value of Tan 0 Degrees?

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

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

Explanation:

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

Methods to Find Value of Tan 0 Degrees

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

• Using Trigonometric Functions
• Using Unit Circle

Tan 0° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 0 degrees as:

• sin(0°)/cos(0°)
• ± sin 0°/√(1 - sin²(0°))
• ± √(1 - cos²(0°))/cos 0°
• ± 1/√(cosec²(0°) - 1)
• ± √(sec²(0°) - 1)
• 1/cot 0°

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

We can use trigonometric identities to represent tan 0° as,

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

Tan 0 Degrees Using Unit Circle

To find the value of tan 0 degrees using the unit circle:

• Draw the radius of unit circle, ‘r’, to form 0° angle with the positive x-axis.
• The tan of 0 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 0° = y/x = 0

☛ Also Check:

• tan 225 degrees
• tan 3 degrees
• tan 12 degrees
• tan 80 degrees
• tan 16 degrees
• tan 51 degrees

FAQs on Tan 0 Degrees

What is Tan 0 Degrees?

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

How to Find the Value of Tan 0 Degrees?

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

What is the Value of Tan 0 Degrees in Terms of Cot 0°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 0° as 1/cot(0°). 

How to Find Tan 0° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 0° can be given in terms of other trigonometric functions as:

• sin(0°)/cos(0°)
• ± sin 0°/√(1 - sin²(0°))
• ± √(1 - cos²(0°))/cos 0°
• ± 1/√(cosec²(0°) - 1)
• ± √(sec²(0°) - 1)
• 1/cot 0°

☛ Also check: trigonometric table

What is the Value of Tan 0° in Terms of Sec 0°?

We can represent the tangent function in terms of the secant function using trig identities, tan 0° can be written as √(sec²(0°) - 1). Here, the value of sec 0° is equal to 1.