Tan 285 Degrees
The value of tan 285 degrees is -3.7320508. . .. Tan 285 degrees in radians is written as tan (285° × π/180°), i.e., tan (19π/12) or tan (4.974188. . .). In this article, we will discuss the methods to find the value of tan 285 degrees with examples.
- Tan 285°: -2 - √3
- Tan 285° in decimal: -3.7320508. . .
- Tan (-285 degrees): 3.7320508. . . or 2 + √3
- Tan 285° in radians: tan (19π/12) or tan (4.9741883 . . .)
What is the Value of Tan 285 Degrees?
The value of tan 285 degrees in decimal is -3.732050807. . .. Tan 285 degrees can also be expressed using the equivalent of the given angle (285 degrees) in radians (4.97418 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 285 degrees = 285° × (π/180°) rad = 19π/12 or 4.9741 . . .
∴ tan 285° = tan(4.9741) = -2 - √3 or -3.7320508. . .
Explanation:
For tan 285 degrees, the angle 285° lies between 270° and 360° (Fourth Quadrant). Since tangent function is negative in the fourth quadrant, thus tan 285° value = -2 - √3 or -3.7320508. . .
Since the tangent function is a periodic function, we can represent tan 285° as, tan 285 degrees = tan(285° + n × 180°), n ∈ Z.
⇒ tan 285° = tan 465° = tan 645°, and so on.
Note: Since, tangent is an odd function, the value of tan(-285°) = -tan(285°).
Methods to Find Value of Tan 285 Degrees
The tangent function is negative in the 4th quadrant. The value of tan 285° is given as -3.73205. . .. We can find the value of tan 285 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 285 Degrees Using Unit Circle
To find the value of tan 285 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 285° angle with the positive x-axis.
- The tan of 285 degrees equals the y-coordinate(-0.9659) divided by x-coordinate(0.2588) of the point of intersection (0.2588, -0.9659) of unit circle and r.
Hence the value of tan 285° = y/x = -3.7321 (approx).
Tan 285° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 285 degrees as:
- sin(285°)/cos(285°)
- ± sin 285°/√(1 - sin²(285°))
- ± √(1 - cos²(285°))/cos 285°
- ± 1/√(cosec²(285°) - 1)
- ± √(sec²(285°) - 1)
- 1/cot 285°
Note: Since 285° lies in the 4th Quadrant, the final value of tan 285° will be negative.
We can use trigonometric identities to represent tan 285° as,
- cot(90° - 285°) = cot(-195°)
- -cot(90° + 285°) = -cot 375°
- -tan (180° - 285°) = -tan(-105°)
☛ Also Check:
FAQs on Tan 285 Degrees
What is Tan 285 Degrees?
Tan 285 degrees is the value of tangent trigonometric function for an angle equal to 285 degrees. The value of tan 285° is -2 - √3 or -3.7321 (approx).
How to Find the Value of Tan 285 Degrees?
The value of tan 285 degrees can be calculated by constructing an angle of 285° with the x-axis, and then finding the coordinates of the corresponding point (0.2588, -0.9659) on the unit circle. The value of tan 285° is equal to the y-coordinate(-0.9659) divided by the x-coordinate (0.2588). ∴ tan 285° = -2 - √3 or -3.7321
What is the Value of Tan 285 Degrees in Terms of Cot 285°?
Since the tangent function is the reciprocal of the cotangent function, we can write tan 285° as 1/cot(285°). The value of cot 285° is equal to -2 + √3.
How to Find Tan 285° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 285° can be given in terms of other trigonometric functions as:
- sin(285°)/cos(285°)
- ± sin 285°/√(1 - sin²(285°))
- ± √(1 - cos²(285°))/cos 285°
- ± 1/√(cosec²(285°) - 1)
- ± √(sec²(285°) - 1)
- 1/cot 285°
☛ Also check: trigonometric table
What is the Exact Value of tan 285 Degrees?
The exact value of tan 285 degrees can be given accurately up to 8 decimal places as -3.73205080 or as -2 - √3.