Tan 72 Degrees

The value of tan 72 degrees is 3.0776835. . .. Tan 72 degrees in radians is written as tan (72° × π/180°), i.e., tan (2π/5) or tan (1.256637. . .). In this article, we will discuss the methods to find the value of tan 72 degrees with examples.

• Tan 72°: √(5 + 2√5)
• Tan 72° in decimal: 3.0776835. . .
• Tan (-72 degrees): -3.0776835. . . or -√(5 + 2√5)
• Tan 72° in radians: tan (2π/5) or tan (1.2566370 . . .)

What is the Value of Tan 72 Degrees?

The value of tan 72 degrees in decimal is 3.077683537. . .. Tan 72 degrees can also be expressed using the equivalent of the given angle (72 degrees) in radians (1.25663 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 72 degrees = 72° × (π/180°) rad = 2π/5 or 1.2566 . . .
∴ tan 72° = tan(1.2566) = √(5 + 2√5) or 3.0776835. . .

Explanation:

For tan 72 degrees, the angle 72° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 72° value = √(5 + 2√5) or 3.0776835. . .
Since the tangent function is a periodic function, we can represent tan 72° as, tan 72 degrees = tan(72° + n × 180°), n ∈ Z.
⇒ tan 72° = tan 252° = tan 432°, and so on.
Note: Since, tangent is an odd function, the value of tan(-72°) = -tan(72°).

Methods to Find Value of Tan 72 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 72° is given as 3.07768. . .. We can find the value of tan 72 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 72° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 72 degrees as:

• sin(72°)/cos(72°)
• ± sin 72°/√(1 - sin²(72°))
• ± √(1 - cos²(72°))/cos 72°
• ± 1/√(cosec²(72°) - 1)
• ± √(sec²(72°) - 1)
• 1/cot 72°

Note: Since 72° lies in the 1st Quadrant, the final value of tan 72° will be positive.

We can use trigonometric identities to represent tan 72° as,

• cot(90° - 72°) = cot 18°
• -cot(90° + 72°) = -cot 162°
• -tan (180° - 72°) = -tan 108°

Tan 72 Degrees Using Unit Circle

To find the value of tan 72 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 72° angle with the positive x-axis.
• The tan of 72 degrees equals the y-coordinate(0.9511) divided by x-coordinate(0.309) of the point of intersection (0.309, 0.9511) of unit circle and r.

Hence the value of tan 72° = y/x = 3.0777 (approx).

☛ Also Check:

• tan 2 degrees
• tan 15 degrees
• tan 0 degrees
• tan 110 degrees
• tan 34 degrees
• tan 2000 degrees

FAQs on Tan 72 Degrees

What is Tan 72 Degrees?

Tan 72 degrees is the value of tangent trigonometric function for an angle equal to 72 degrees. The value of tan 72° is √(5 + 2√5) or 3.0777 (approx).

How to Find the Value of Tan 72 Degrees?

The value of tan 72 degrees can be calculated by constructing an angle of 72° with the x-axis, and then finding the coordinates of the corresponding point (0.309, 0.9511) on the unit circle. The value of tan 72° is equal to the y-coordinate(0.9511) divided by the x-coordinate (0.309). ∴ tan 72° = √(5 + 2√5) or 3.0777

What is the Exact Value of tan 72 Degrees?

The exact value of tan 72 degrees can be given accurately up to 8 decimal places as 3.07768353 or as √(5 + 2√5).

How to Find Tan 72° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 72° can be given in terms of other trigonometric functions as:

• sin(72°)/cos(72°)
• ± sin 72°/√(1 - sin²(72°))
• ± √(1 - cos²(72°))/cos 72°
• ± 1/√(cosec²(72°) - 1)
• ± √(sec²(72°) - 1)
• 1/cot 72°

☛ Also check: trigonometric table

What is the Value of Tan 72 Degrees in Terms of Sin 72°?

Using trigonometric identities, we can write tan 72° in terms of sin 72° as, tan(72°) = sin 72°/√(1 - sin²(72°)) . Here, the value of sin 72° is equal to √(10 - 2√5)/2.