Tan 85 Degrees
The value of tan 85 degrees is 11.4300523. . .. Tan 85 degrees in radians is written as tan (85° × π/180°), i.e., tan (17π/36) or tan (1.483529. . .). In this article, we will discuss the methods to find the value of tan 85 degrees with examples.
- Tan 85° in decimal: 11.4300523. . .
- Tan (-85 degrees): -11.4300523. . .
- Tan 85° in radians: tan (17π/36) or tan (1.4835298 . . .)
What is the Value of Tan 85 Degrees?
The value of tan 85 degrees in decimal is 11.430052302. . .. Tan 85 degrees can also be expressed using the equivalent of the given angle (85 degrees) in radians (1.48352 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 85 degrees = 85° × (π/180°) rad = 17π/36 or 1.4835 . . .
∴ tan 85° = tan(1.4835) = 11.4300523. . .
Explanation:
For tan 85 degrees, the angle 85° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 85° value = 11.4300523. . .
Since the tangent function is a periodic function, we can represent tan 85° as, tan 85 degrees = tan(85° + n × 180°), n ∈ Z.
⇒ tan 85° = tan 265° = tan 445°, and so on.
Note: Since, tangent is an odd function, the value of tan(-85°) = -tan(85°).
Methods to Find Value of Tan 85 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 85° is given as 11.43005. . .. We can find the value of tan 85 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 85° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 85 degrees as:
- sin(85°)/cos(85°)
- ± sin 85°/√(1 - sin²(85°))
- ± √(1 - cos²(85°))/cos 85°
- ± 1/√(cosec²(85°) - 1)
- ± √(sec²(85°) - 1)
- 1/cot 85°
Note: Since 85° lies in the 1st Quadrant, the final value of tan 85° will be positive.
We can use trigonometric identities to represent tan 85° as,
- cot(90° - 85°) = cot 5°
- -cot(90° + 85°) = -cot 175°
- -tan (180° - 85°) = -tan 95°
Tan 85 Degrees Using Unit Circle
To find the value of tan 85 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 85° angle with the positive x-axis.
- The tan of 85 degrees equals the y-coordinate(0.9962) divided by x-coordinate(0.0872) of the point of intersection (0.0872, 0.9962) of unit circle and r.
Hence the value of tan 85° = y/x = 11.4301 (approx).
☛ Also Check:
FAQs on Tan 85 Degrees
What is Tan 85 Degrees?
Tan 85 degrees is the value of tangent trigonometric function for an angle equal to 85 degrees. The value of tan 85° is 11.4301 (approx).
How to Find the Value of Tan 85 Degrees?
The value of tan 85 degrees can be calculated by constructing an angle of 85° with the x-axis, and then finding the coordinates of the corresponding point (0.0872, 0.9962) on the unit circle. The value of tan 85° is equal to the y-coordinate(0.9962) divided by the x-coordinate (0.0872). ∴ tan 85° = 11.4301
What is the Exact Value of tan 85 Degrees?
The exact value of tan 85 degrees can be given accurately up to 8 decimal places as 11.43005230.
What is the Value of Tan 85 Degrees in Terms of Cos 85°?
We know, using trig identities, we can write tan 85° as √(1 - cos²(85°))/cos 85°. Here, the value of cos 85° is equal to 0.087155.
How to Find Tan 85° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 85° can be given in terms of other trigonometric functions as:
- sin(85°)/cos(85°)
- ± sin 85°/√(1 - sin²(85°))
- ± √(1 - cos²(85°))/cos 85°
- ± 1/√(cosec²(85°) - 1)
- ± √(sec²(85°) - 1)
- 1/cot 85°
☛ Also check: trigonometric table