Tan 1260 Degrees
The value of tan 1260 degrees is 0. Tan 1260 degrees in radians is written as tan (1260° × π/180°), i.e., tan (7π) or tan (21.991148. . .). In this article, we will discuss the methods to find the value of tan 1260 degrees with examples.
- Tan 1260°: 0
- Tan (-1260 degrees): 0
- Tan 1260° in radians: tan (7π) or tan (21.9911485 . . .)
What is the Value of Tan 1260 Degrees?
The value of tan 1260 degrees is 0. Tan 1260 degrees can also be expressed using the equivalent of the given angle (1260 degrees) in radians (21.99114 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 1260 degrees = 1260° × (π/180°) rad = 7π or 21.9911 . . .
∴ tan 1260° = tan(21.9911) = 0
Explanation:
For tan 1260°, the angle 1260° > 360°. We can represent tan 1260° as, tan(1260° mod 360°) = tan(180°). The angle 1260°, coterminal to angle 180°, lies on the negative x-axis.
Thus, tan 1260 degrees value = 0
Similarly, given the periodic property of tan 1260°, it can also be written as, tan 1260 degrees = (1260° + n × 180°), n ∈ Z.
⇒ tan 1260° = tan 1440° = tan 1620°, and so on.
Note: Since, tangent is an odd function, the value of tan(-1260°) = -tan(1260°) = 0.
Methods to Find Value of Tan 1260 Degrees
The value of tan 1260° is given as 0. We can find the value of tan 1260 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 1260° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 1260 degrees as:
- sin(1260°)/cos(1260°)
- ± sin 1260°/√(1 - sin²(1260°))
- ± √(1 - cos²(1260°))/cos 1260°
- ± 1/√(cosec²(1260°) - 1)
- ± √(sec²(1260°) - 1)
- 1/cot 1260°
Note: Since 1260° lies on the negative x-axis, the final value of tan 1260° is 0.
We can use trigonometric identities to represent tan 1260° as,
- cot(90° - 1260°) = cot(-1170°)
- -cot(90° + 1260°) = -cot 1350°
- -tan (180° - 1260°) = -tan(-1080°)
Tan 1260 Degrees Using Unit Circle
To find the value of tan 1260 degrees using the unit circle, represent 1260° in the form (3 × 360°) + 180° [∵ 1260°>360°] ∵ The angle 1260° is coterminal to 180° angle and also tangent is a periodic function, tan 1260° = tan 180°.
- Rotate ‘r’ anticlockwise to form 180° or 1260° angle with the positive x-axis.
- The tan of 1260 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 1260° = y/x = 0
☛ Also Check:
FAQs on Tan 1260 Degrees
What is Tan 1260 Degrees?
Tan 1260 degrees is the value of tangent trigonometric function for an angle equal to 1260 degrees. The value of tan 1260° is 0.
What is the Value of Tan 1260° in Terms of Cosec 1260°?
Since the tangent function can be represented using the cosecant function, we can write tan 1260° as 1/√(cosec²(1260°) - 1).
How to Find the Value of Tan 1260 Degrees?
The value of tan 1260 degrees can be calculated by constructing an angle of 1260° with the x-axis, and then finding the coordinates of the corresponding point (-1, 0) on the unit circle. The value of tan 1260° is equal to the y-coordinate(0) divided by the x-coordinate (-1). ∴ tan 1260° = 0
How to Find Tan 1260° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 1260° can be given in terms of other trigonometric functions as:
- sin(1260°)/cos(1260°)
- ± sin 1260°/√(1 - sin²(1260°))
- ± √(1 - cos²(1260°))/cos 1260°
- ± 1/√(cosec²(1260°) - 1)
- ± √(sec²(1260°) - 1)
- 1/cot 1260°
☛ Also check: trigonometry table
What is the Value of Tan 1260 Degrees in Terms of Sin 1260°?
Using trigonometric identities, we can write tan 1260° in terms of sin 1260° as, tan(1260°) = sin 1260°/√(1 - sin²(1260°)) . Here, the value of sin 1260° is equal to 0.