Tan 81 Degrees
The value of tan 81 degrees is 6.3137515. . .. Tan 81 degrees in radians is written as tan (81° × π/180°), i.e., tan (9π/20) or tan (1.413716. . .). In this article, we will discuss the methods to find the value of tan 81 degrees with examples.
- Tan 81° in decimal: 6.3137515. . .
- Tan (-81 degrees): -6.3137515. . .
- Tan 81° in radians: tan (9π/20) or tan (1.4137166 . . .)
What is the Value of Tan 81 Degrees?
The value of tan 81 degrees in decimal is 6.313751514. . .. Tan 81 degrees can also be expressed using the equivalent of the given angle (81 degrees) in radians (1.41371 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 81 degrees = 81° × (π/180°) rad = 9π/20 or 1.4137 . . .
∴ tan 81° = tan(1.4137) = 6.3137515. . .
Explanation:
For tan 81 degrees, the angle 81° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 81° value = 6.3137515. . .
Since the tangent function is a periodic function, we can represent tan 81° as, tan 81 degrees = tan(81° + n × 180°), n ∈ Z.
⇒ tan 81° = tan 261° = tan 441°, and so on.
Note: Since, tangent is an odd function, the value of tan(-81°) = -tan(81°).
Methods to Find Value of Tan 81 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 81° is given as 6.31375. . .. We can find the value of tan 81 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 81° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 81 degrees as:
- sin(81°)/cos(81°)
- ± sin 81°/√(1 - sin²(81°))
- ± √(1 - cos²(81°))/cos 81°
- ± 1/√(cosec²(81°) - 1)
- ± √(sec²(81°) - 1)
- 1/cot 81°
Note: Since 81° lies in the 1st Quadrant, the final value of tan 81° will be positive.
We can use trigonometric identities to represent tan 81° as,
- cot(90° - 81°) = cot 9°
- -cot(90° + 81°) = -cot 171°
- -tan (180° - 81°) = -tan 99°
Tan 81 Degrees Using Unit Circle
To find the value of tan 81 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 81° angle with the positive x-axis.
- The tan of 81 degrees equals the y-coordinate(0.9877) divided by x-coordinate(0.1564) of the point of intersection (0.1564, 0.9877) of unit circle and r.
Hence the value of tan 81° = y/x = 6.3138 (approx).
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FAQs on Tan 81 Degrees
What is Tan 81 Degrees?
Tan 81 degrees is the value of tangent trigonometric function for an angle equal to 81 degrees. The value of tan 81° is 6.3138 (approx).
What is the Value of Tan 81 Degrees in Terms of Cos 81°?
We know, using trig identities, we can write tan 81° as √(1 - cos²(81°))/cos 81°. Here, the value of cos 81° is equal to 0.156434.
What is the Value of Tan 81° in Terms of Sec 81°?
We can represent the tangent function in terms of the secant function using trig identities, tan 81° can be written as √(sec²(81°) - 1). Here, the value of sec 81° is equal to 6.3924.
How to Find the Value of Tan 81 Degrees?
The value of tan 81 degrees can be calculated by constructing an angle of 81° with the x-axis, and then finding the coordinates of the corresponding point (0.1564, 0.9877) on the unit circle. The value of tan 81° is equal to the y-coordinate(0.9877) divided by the x-coordinate (0.1564). ∴ tan 81° = 6.3138
How to Find Tan 81° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 81° can be given in terms of other trigonometric functions as:
- sin(81°)/cos(81°)
- ± sin 81°/√(1 - sin²(81°))
- ± √(1 - cos²(81°))/cos 81°
- ± 1/√(cosec²(81°) - 1)
- ± √(sec²(81°) - 1)
- 1/cot 81°
☛ Also check: trigonometric table