Tan 36 Degrees
The value of tan 36 degrees is 0.7265425. . .. Tan 36 degrees in radians is written as tan (36° × π/180°), i.e., tan (π/5) or tan (0.628318. . .). In this article, we will discuss the methods to find the value of tan 36 degrees with examples.
 Tan 36°: √(5  2√5)
 Tan 36° in decimal: 0.7265425. . .
 Tan (36 degrees): 0.7265425. . . or √(5  2√5)
 Tan 36° in radians: tan (π/5) or tan (0.6283185 . . .)
What is the Value of Tan 36 Degrees?
The value of tan 36 degrees in decimal is 0.726542528. . .. Tan 36 degrees can also be expressed using the equivalent of the given angle (36 degrees) in radians (0.62831 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 36 degrees = 36° × (π/180°) rad = π/5 or 0.6283 . . .
∴ tan 36° = tan(0.6283) = √(5  2√5) or 0.7265425. . .
Explanation:
For tan 36 degrees, the angle 36° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 36° value = √(5  2√5) or 0.7265425. . .
Since the tangent function is a periodic function, we can represent tan 36° as, tan 36 degrees = tan(36° + n × 180°), n ∈ Z.
⇒ tan 36° = tan 216° = tan 396°, and so on.
Note: Since, tangent is an odd function, the value of tan(36°) = tan(36°).
Methods to Find Value of Tan 36 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 36° is given as 0.72654. . .. We can find the value of tan 36 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Tan 36 Degrees Using Unit Circle
To find the value of tan 36 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 36° angle with the positive xaxis.
 The tan of 36 degrees equals the ycoordinate(0.5878) divided by xcoordinate(0.809) of the point of intersection (0.809, 0.5878) of unit circle and r.
Hence the value of tan 36° = y/x = 0.7265 (approx).
Tan 36° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 36 degrees as:
 sin(36°)/cos(36°)
 ± sin 36°/√(1  sin²(36°))
 ± √(1  cos²(36°))/cos 36°
 ± 1/√(cosec²(36°)  1)
 ± √(sec²(36°)  1)
 1/cot 36°
Note: Since 36° lies in the 1st Quadrant, the final value of tan 36° will be positive.
We can use trigonometric identities to represent tan 36° as,
 cot(90°  36°) = cot 54°
 cot(90° + 36°) = cot 126°
 tan (180°  36°) = tan 144°
☛ Also Check:
Examples Using Tan 36 Degrees

Example 1: Find the value of tan 36° if cot 36° is 1.3763.
Solution:
Since, tan 36° = 1/cot 36°
⇒ tan 36° = 1/1.3763 = 0.7265 
Example 2: Find the value of 3 tan(36°)/7 tan(144°).
Solution:
Using trigonometric identities, we know, tan(36°) = tan(180°  36°) = tan 144°.
⇒ tan(36°) = tan(144°)
⇒ Value of 3 tan(36°)/7 tan(144°) = 3/7 
Example 3: Simplify: 3 (tan 36°/cot 54°)
Solution:
We know tan 36° = cot 54°
⇒ 3 tan 36°/cot 54° = 3 (tan 36°/tan 36°)
= 3(1) = 3
FAQs on Tan 36 Degrees
What is Tan 36 Degrees?
Tan 36 degrees is the value of tangent trigonometric function for an angle equal to 36 degrees. The value of tan 36° is √(5  2√5) or 0.7265 (approx).
How to Find Tan 36° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 36° can be given in terms of other trigonometric functions as:
 sin(36°)/cos(36°)
 ± sin 36°/√(1  sin²(36°))
 ± √(1  cos²(36°))/cos 36°
 ± 1/√(cosec²(36°)  1)
 ± √(sec²(36°)  1)
 1/cot 36°
☛ Also check: trigonometric table
How to Find the Value of Tan 36 Degrees?
The value of tan 36 degrees can be calculated by constructing an angle of 36° with the xaxis, and then finding the coordinates of the corresponding point (0.809, 0.5878) on the unit circle. The value of tan 36° is equal to the ycoordinate(0.5878) divided by the xcoordinate (0.809). ∴ tan 36° = √(5  2√5) or 0.7265
What is the Value of Tan 36 Degrees in Terms of Sin 36°?
Using trigonometric identities, we can write tan 36° in terms of sin 36° as, tan(36°) = sin 36°/√(1  sin²(36°)) . Here, the value of sin 36° is equal to √(10  2√5)/4.
What is the Value of Tan 36° in Terms of Sec 36°?
We can represent the tangent function in terms of the secant function using trig identities, tan 36° can be written as √(sec²(36°)  1). Here, the value of sec 36° is equal to 1.2360.
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