Tan 140 Degrees
The value of tan 140 degrees is -0.8390996. . .. Tan 140 degrees in radians is written as tan (140° × π/180°), i.e., tan (7π/9) or tan (2.443460. . .). In this article, we will discuss the methods to find the value of tan 140 degrees with examples.
- Tan 140° in decimal: -0.8390996. . .
- Tan (-140 degrees): 0.8390996. . .
- Tan 140° in radians: tan (7π/9) or tan (2.4434609 . . .)
What is the Value of Tan 140 Degrees?
The value of tan 140 degrees in decimal is -0.839099631. . .. Tan 140 degrees can also be expressed using the equivalent of the given angle (140 degrees) in radians (2.44346 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 140 degrees = 140° × (π/180°) rad = 7π/9 or 2.4434 . . .
∴ tan 140° = tan(2.4434) = -0.8390996. . .
Explanation:
For tan 140 degrees, the angle 140° lies between 90° and 180° (Second Quadrant). Since tangent function is negative in the second quadrant, thus tan 140° value = -0.8390996. . .
Since the tangent function is a periodic function, we can represent tan 140° as, tan 140 degrees = tan(140° + n × 180°), n ∈ Z.
⇒ tan 140° = tan 320° = tan 500°, and so on.
Note: Since, tangent is an odd function, the value of tan(-140°) = -tan(140°).
Methods to Find Value of Tan 140 Degrees
The tangent function is negative in the 2nd quadrant. The value of tan 140° is given as -0.83909. . .. We can find the value of tan 140 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 140° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 140 degrees as:
- sin(140°)/cos(140°)
- ± sin 140°/√(1 - sin²(140°))
- ± √(1 - cos²(140°))/cos 140°
- ± 1/√(cosec²(140°) - 1)
- ± √(sec²(140°) - 1)
- 1/cot 140°
Note: Since 140° lies in the 2nd Quadrant, the final value of tan 140° will be negative.
We can use trigonometric identities to represent tan 140° as,
- cot(90° - 140°) = cot(-50°)
- -cot(90° + 140°) = -cot 230°
- -tan (180° - 140°) = -tan 40°
Tan 140 Degrees Using Unit Circle
To find the value of tan 140 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 140° angle with the positive x-axis.
- The tan of 140 degrees equals the y-coordinate(0.6428) divided by x-coordinate(-0.766) of the point of intersection (-0.766, 0.6428) of unit circle and r.
Hence the value of tan 140° = y/x = -0.8391 (approx).
☛ Also Check:
FAQs on Tan 140 Degrees
What is Tan 140 Degrees?
Tan 140 degrees is the value of tangent trigonometric function for an angle equal to 140 degrees. The value of tan 140° is -0.8391 (approx).
How to Find Tan 140° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 140° can be given in terms of other trigonometric functions as:
- sin(140°)/cos(140°)
- ± sin 140°/√(1 - sin²(140°))
- ± √(1 - cos²(140°))/cos 140°
- ± 1/√(cosec²(140°) - 1)
- ± √(sec²(140°) - 1)
- 1/cot 140°
☛ Also check: trigonometry table
What is the Value of Tan 140 Degrees in Terms of Cot 140°?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 140° as 1/cot(140°). The value of cot 140° is equal to -1.19175.
What is the Value of Tan 140° in Terms of Cosec 140°?
Since the tangent function can be represented using the cosecant function, we can write tan 140° as -1/√(cosec²(140°) - 1). The value of cosec 140° is equal to 1.55572.
How to Find the Value of Tan 140 Degrees?
The value of tan 140 degrees can be calculated by constructing an angle of 140° with the x-axis, and then finding the coordinates of the corresponding point (-0.766, 0.6428) on the unit circle. The value of tan 140° is equal to the y-coordinate(0.6428) divided by the x-coordinate (-0.766). ∴ tan 140° = -0.8391