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Tan 86 Degrees

The value of tan 86 degrees is 14.3006662. . .. Tan 86 degrees in radians is written as tan (86° × π/180°), i.e., tan (43π/90) or tan (1.500983. . .). In this article, we will discuss the methods to find the value of tan 86 degrees with examples.

Tan 86° in decimal: 14.3006662. . .
Tan (-86 degrees): -14.3006662. . .
Tan 86° in radians: tan (43π/90) or tan (1.5009831 . . .)

What is the Value of Tan 86 Degrees?

The value of tan 86 degrees in decimal is 14.300666256. . .. Tan 86 degrees can also be expressed using the equivalent of the given angle (86 degrees) in radians (1.50098 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 86 degrees = 86° × (π/180°) rad = 43π/90 or 1.5009 . . .
∴ tan 86° = tan(1.5009) = 14.3006662. . .

Explanation:

For tan 86 degrees, the angle 86° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 86° value = 14.3006662. . .
Since the tangent function is a periodic function, we can represent tan 86° as, tan 86 degrees = tan(86° + n × 180°), n ∈ Z.
⇒ tan 86° = tan 266° = tan 446°, and so on.
Note: Since, tangent is an odd function, the value of tan(-86°) = -tan(86°).

Methods to Find Value of Tan 86 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 86° is given as 14.30066. . .. We can find the value of tan 86 degrees by:

Using Unit Circle
Using Trigonometric Functions

Tan 86 Degrees Using Unit Circle

To find the value of tan 86 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 86° angle with the positive x-axis.
The tan of 86 degrees equals the y-coordinate(0.9976) divided by x-coordinate(0.0698) of the point of intersection (0.0698, 0.9976) of unit circle and r.

Hence the value of tan 86° = y/x = 14.3007 (approx).

Tan 86° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 86 degrees as:

sin(86°)/cos(86°)
± sin 86°/√(1 - sin²(86°))
± √(1 - cos²(86°))/cos 86°
± 1/√(cosec²(86°) - 1)
± √(sec²(86°) - 1)
1/cot 86°

Note: Since 86° lies in the 1st Quadrant, the final value of tan 86° will be positive.

We can use trigonometric identities to represent tan 86° as,

cot(90° - 86°) = cot 4°
-cot(90° + 86°) = -cot 176°
-tan (180° - 86°) = -tan 94°

☛ Also Check:

Examples Using Tan 86 Degrees

Example 1: Find the value of 5 tan(86°)/6 tan(94°).

Solution:

Using trigonometric identities, we know, tan(86°) = -tan(180° - 86°) = -tan 94°.
⇒ tan(86°) = -tan(94°)
⇒ Value of 5 tan(86°)/6 tan(94°) = -5/6
Example 2: Find the value of 2 tan 43°/(1 - tan²(43°)). [Hint: Use tan 86° = 14.3007]

Solution:

Using the tan 2a formula,
2 tan 43°/(1 - tan²(43°)) = tan(2 × 43°) = tan 86°
∵ tan 86° = 14.3007
⇒ 2 tan 43°/(1 - tan²(43°)) = 14.3007
Example 3: Simplify: 6 (tan 86°/cot 4°)

Solution:

We know tan 86° = cot 4°
⇒ 6 tan 86°/cot 4° = 6 (tan 86°/tan 86°)
= 6(1) = 6

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FAQs on Tan 86 Degrees

What is Tan 86 Degrees?

Tan 86 degrees is the value of tangent trigonometric function for an angle equal to 86 degrees. The value of tan 86° is 14.3007 (approx).

What is the Value of Tan 86° in Terms of Cosec 86°?

Since the tangent function can be represented using the cosecant function, we can write tan 86° as 1/√(cosec²(86°) - 1). The value of cosec 86° is equal to 1.00244.

What is the Value of Tan 86 Degrees in Terms of Sin 86°?

Using trigonometric identities, we can write tan 86° in terms of sin 86° as, tan(86°) = sin 86°/√(1 - sin²(86°)) . Here, the value of sin 86° is equal to 0.9976.

How to Find Tan 86° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 86° can be given in terms of other trigonometric functions as:

sin(86°)/cos(86°)
± sin 86°/√(1 - sin²(86°))
± √(1 - cos²(86°))/cos 86°
± 1/√(cosec²(86°) - 1)
± √(sec²(86°) - 1)
1/cot 86°

☛ Also check: trigonometric table

How to Find the Value of Tan 86 Degrees?

The value of tan 86 degrees can be calculated by constructing an angle of 86° with the x-axis, and then finding the coordinates of the corresponding point (0.0698, 0.9976) on the unit circle. The value of tan 86° is equal to the y-coordinate(0.9976) divided by the x-coordinate (0.0698). ∴ tan 86° = 14.3007

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