Tan 82 Degrees
The value of tan 82 degrees is 7.1153697. . .. Tan 82 degrees in radians is written as tan (82° × π/180°), i.e., tan (41π/90) or tan (1.431169. . .). In this article, we will discuss the methods to find the value of tan 82 degrees with examples.
- Tan 82° in decimal: 7.1153697. . .
- Tan (-82 degrees): -7.1153697. . .
- Tan 82° in radians: tan (41π/90) or tan (1.4311699 . . .)
What is the Value of Tan 82 Degrees?
The value of tan 82 degrees in decimal is 7.115369722. . .. Tan 82 degrees can also be expressed using the equivalent of the given angle (82 degrees) in radians (1.43116 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 82 degrees = 82° × (π/180°) rad = 41π/90 or 1.4311 . . .
∴ tan 82° = tan(1.4311) = 7.1153697. . .
Explanation:
For tan 82 degrees, the angle 82° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 82° value = 7.1153697. . .
Since the tangent function is a periodic function, we can represent tan 82° as, tan 82 degrees = tan(82° + n × 180°), n ∈ Z.
⇒ tan 82° = tan 262° = tan 442°, and so on.
Note: Since, tangent is an odd function, the value of tan(-82°) = -tan(82°).
Methods to Find Value of Tan 82 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 82° is given as 7.11536. . .. We can find the value of tan 82 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 82 Degrees Using Unit Circle
To find the value of tan 82 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 82° angle with the positive x-axis.
- The tan of 82 degrees equals the y-coordinate(0.9903) divided by x-coordinate(0.1392) of the point of intersection (0.1392, 0.9903) of unit circle and r.
Hence the value of tan 82° = y/x = 7.1154 (approx).
Tan 82° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 82 degrees as:
- sin(82°)/cos(82°)
- ± sin 82°/√(1 - sin²(82°))
- ± √(1 - cos²(82°))/cos 82°
- ± 1/√(cosec²(82°) - 1)
- ± √(sec²(82°) - 1)
- 1/cot 82°
Note: Since 82° lies in the 1st Quadrant, the final value of tan 82° will be positive.
We can use trigonometric identities to represent tan 82° as,
- cot(90° - 82°) = cot 8°
- -cot(90° + 82°) = -cot 172°
- -tan (180° - 82°) = -tan 98°
☛ Also Check:
FAQs on Tan 82 Degrees
What is Tan 82 Degrees?
Tan 82 degrees is the value of tangent trigonometric function for an angle equal to 82 degrees. The value of tan 82° is 7.1154 (approx).
What is the Value of Tan 82° in Terms of Sec 82°?
We can represent the tangent function in terms of the secant function using trig identities, tan 82° can be written as √(sec²(82°) - 1). Here, the value of sec 82° is equal to 7.1852.
How to Find the Value of Tan 82 Degrees?
The value of tan 82 degrees can be calculated by constructing an angle of 82° with the x-axis, and then finding the coordinates of the corresponding point (0.1392, 0.9903) on the unit circle. The value of tan 82° is equal to the y-coordinate(0.9903) divided by the x-coordinate (0.1392). ∴ tan 82° = 7.1154
What is the Value of Tan 82 Degrees in Terms of Sin 82°?
Using trigonometric identities, we can write tan 82° in terms of sin 82° as, tan(82°) = sin 82°/√(1 - sin²(82°)) . Here, the value of sin 82° is equal to 0.9903.
How to Find Tan 82° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 82° can be given in terms of other trigonometric functions as:
- sin(82°)/cos(82°)
- ± sin 82°/√(1 - sin²(82°))
- ± √(1 - cos²(82°))/cos 82°
- ± 1/√(cosec²(82°) - 1)
- ± √(sec²(82°) - 1)
- 1/cot 82°
☛ Also check: trigonometric table