Tan 65 Degrees
The value of tan 65 degrees is 2.1445069. . .. Tan 65 degrees in radians is written as tan (65° × π/180°), i.e., tan (13π/36) or tan (1.134464. . .). In this article, we will discuss the methods to find the value of tan 65 degrees with examples.
 Tan 65° in decimal: 2.1445069. . .
 Tan (65 degrees): 2.1445069. . .
 Tan 65° in radians: tan (13π/36) or tan (1.1344640 . . .)
What is the Value of Tan 65 Degrees?
The value of tan 65 degrees in decimal is 2.144506920. . .. Tan 65 degrees can also be expressed using the equivalent of the given angle (65 degrees) in radians (1.13446 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 65 degrees = 65° × (π/180°) rad = 13π/36 or 1.1344 . . .
∴ tan 65° = tan(1.1344) = 2.1445069. . .
Explanation:
For tan 65 degrees, the angle 65° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 65° value = 2.1445069. . .
Since the tangent function is a periodic function, we can represent tan 65° as, tan 65 degrees = tan(65° + n × 180°), n ∈ Z.
⇒ tan 65° = tan 245° = tan 425°, and so on.
Note: Since, tangent is an odd function, the value of tan(65°) = tan(65°).
Methods to Find Value of Tan 65 Degrees
The tangent function is positive in the 1st quadrant. The value of tan 65° is given as 2.14450. . .. We can find the value of tan 65 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Tan 65° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 65 degrees as:
 sin(65°)/cos(65°)
 ± sin 65°/√(1  sin²(65°))
 ± √(1  cos²(65°))/cos 65°
 ± 1/√(cosec²(65°)  1)
 ± √(sec²(65°)  1)
 1/cot 65°
Note: Since 65° lies in the 1st Quadrant, the final value of tan 65° will be positive.
We can use trigonometric identities to represent tan 65° as,
 cot(90°  65°) = cot 25°
 cot(90° + 65°) = cot 155°
 tan (180°  65°) = tan 115°
Tan 65 Degrees Using Unit Circle
To find the value of tan 65 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 65° angle with the positive xaxis.
 The tan of 65 degrees equals the ycoordinate(0.9063) divided by xcoordinate(0.4226) of the point of intersection (0.4226, 0.9063) of unit circle and r.
Hence the value of tan 65° = y/x = 2.1445 (approx).
☛ Also Check:
Examples Using Tan 65 Degrees

Example 1: Find the value of 2 tan 32.5°/(1  tan²(32.5°)). [Hint: Use tan 65° = 2.1445]
Solution:
Using the tan 2a formula,
2 tan 32.5°/(1  tan²(32.5°)) = tan(2 × 32.5°) = tan 65°
∵ tan 65° = 2.1445
⇒ 2 tan 32.5°/(1  tan²(32.5°)) = 2.1445 
Example 2: Find the value of tan 65° if cot 65° is 0.4663.
Solution:
Since, tan 65° = 1/cot 65°
⇒ tan 65° = 1/0.4663 = 2.1445 
Example 3: Using the value of tan 65°, solve: (sec²(65°)  1).
Solution:
We know, (sec²(65°)  1) = (tan²(65°)) = 4.5989
⇒ (sec²(65°)  1) = 4.5989
FAQs on Tan 65 Degrees
What is Tan 65 Degrees?
Tan 65 degrees is the value of tangent trigonometric function for an angle equal to 65 degrees. The value of tan 65° is 2.1445 (approx).
How to Find Tan 65° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 65° can be given in terms of other trigonometric functions as:
 sin(65°)/cos(65°)
 ± sin 65°/√(1  sin²(65°))
 ± √(1  cos²(65°))/cos 65°
 ± 1/√(cosec²(65°)  1)
 ± √(sec²(65°)  1)
 1/cot 65°
☛ Also check: trigonometry table
What is the Value of Tan 65° in Terms of Cosec 65°?
Since the tangent function can be represented using the cosecant function, we can write tan 65° as 1/√(cosec²(65°)  1). The value of cosec 65° is equal to 1.10337.
What is the Value of Tan 65 Degrees in Terms of Sin 65°?
Using trigonometric identities, we can write tan 65° in terms of sin 65° as, tan(65°) = sin 65°/√(1  sin²(65°)) . Here, the value of sin 65° is equal to 0.9063.
How to Find the Value of Tan 65 Degrees?
The value of tan 65 degrees can be calculated by constructing an angle of 65° with the xaxis, and then finding the coordinates of the corresponding point (0.4226, 0.9063) on the unit circle. The value of tan 65° is equal to the ycoordinate(0.9063) divided by the xcoordinate (0.4226). ∴ tan 65° = 2.1445
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