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 xaxis. 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 xaxis, 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 xaxis.
 The tan of 0 degrees equals the ycoordinate(0) divided by xcoordinate(1) of the point of intersection (1, 0) of unit circle and r.
Hence the value of tan 0° = y/x = 0
☛ Also Check:
Examples Using Tan 0 Degrees

Example 1: Find the value of 3 tan(0°)/7 tan(45°).
Solution:
Using trigonometric values, we know, tan(0°) = 0 and tan 45° = 1.
⇒ Value of 3 tan(0°)/7 tan(45°) = 0 
Example 2: Find the value of (tan 0° + cos 0°). [Hint: Use tan 0° = 0]
Solution:
∵ tan 0° = 0 and cos 0° = 1
⇒ (tan 0° + cos 0°) = 0 + 1 = 1 
Example 3: Find the value of tan 0° + cot 45°.
Solution:
Since, tan 0° = 0 and cot 45° = 1
⇒ tan 0° + cot 45° = 0 + 1 = 1
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 xaxis, and then finding the coordinates of the corresponding point (1, 0) on the unit circle. The value of tan 0° is equal to the ycoordinate(0) divided by the xcoordinate (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.
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