Tan 31 Degrees

The value of tan 31 degrees is 0.6008606. . .. Tan 31 degrees in radians is written as tan (31° × π/180°), i.e., tan (0.541052. . .). In this article, we will discuss the methods to find the value of tan 31 degrees with examples.

• Tan 31° in decimal: 0.6008606. . .
• Tan (-31 degrees): -0.6008606. . .
• Tan 31° in radians: tan (0.5410520 . . .)

What is the Value of Tan 31 Degrees?

The value of tan 31 degrees in decimal is 0.600860619. . .. Tan 31 degrees can also be expressed using the equivalent of the given angle (31 degrees) in radians (0.54105 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 31 degrees = 31° × (π/180°) rad = 0.5410 . . .
∴ tan 31° = tan(0.5410) = 0.6008606. . .

Explanation:

For tan 31 degrees, the angle 31° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 31° value = 0.6008606. . .
Since the tangent function is a periodic function, we can represent tan 31° as, tan 31 degrees = tan(31° + n × 180°), n ∈ Z.
⇒ tan 31° = tan 211° = tan 391°, and so on.
Note: Since, tangent is an odd function, the value of tan(-31°) = -tan(31°).

Methods to Find Value of Tan 31 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 31° is given as 0.60086. . .. We can find the value of tan 31 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 31° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 31 degrees as:

• sin(31°)/cos(31°)
• ± sin 31°/√(1 - sin²(31°))
• ± √(1 - cos²(31°))/cos 31°
• ± 1/√(cosec²(31°) - 1)
• ± √(sec²(31°) - 1)
• 1/cot 31°

Note: Since 31° lies in the 1st Quadrant, the final value of tan 31° will be positive.

We can use trigonometric identities to represent tan 31° as,

• cot(90° - 31°) = cot 59°
• -cot(90° + 31°) = -cot 121°
• -tan (180° - 31°) = -tan 149°

Tan 31 Degrees Using Unit Circle

To find the value of tan 31 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 31° angle with the positive x-axis.
• The tan of 31 degrees equals the y-coordinate(0.515) divided by x-coordinate(0.8572) of the point of intersection (0.8572, 0.515) of unit circle and r.

Hence the value of tan 31° = y/x = 0.6009 (approx).

☛ Also Check:

• tan 40 degrees
• tan 50 degrees
• tan 90 degrees
• tan 72 degrees
• tan 765 degrees
• tan 570 degrees

FAQs on Tan 31 Degrees

What is Tan 31 Degrees?

Tan 31 degrees is the value of tangent trigonometric function for an angle equal to 31 degrees. The value of tan 31° is 0.6009 (approx).

How to Find Tan 31° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 31° can be given in terms of other trigonometric functions as:

• sin(31°)/cos(31°)
• ± sin 31°/√(1 - sin²(31°))
• ± √(1 - cos²(31°))/cos 31°
• ± 1/√(cosec²(31°) - 1)
• ± √(sec²(31°) - 1)
• 1/cot 31°

☛ Also check: trigonometry table

How to Find the Value of Tan 31 Degrees?

The value of tan 31 degrees can be calculated by constructing an angle of 31° with the x-axis, and then finding the coordinates of the corresponding point (0.8572, 0.515) on the unit circle. The value of tan 31° is equal to the y-coordinate(0.515) divided by the x-coordinate (0.8572). ∴ tan 31° = 0.6009

What is the Value of Tan 31 Degrees in Terms of Cos 31°?

We know, using trig identities, we can write tan 31° as √(1 - cos²(31°))/cos 31°. Here, the value of cos 31° is equal to 0.857167.

What is the Value of Tan 31° in Terms of Cosec 31°?

Since the tangent function can be represented using the cosecant function, we can write tan 31° as 1/√(cosec²(31°) - 1). The value of cosec 31° is equal to 1.94160.