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 x-axis.
• The tan of 65 degrees equals the y-coordinate(0.9063) divided by x-coordinate(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:

• tan 135 degrees
• tan 30 degrees
• tan 15 degrees
• tan 900 degrees
• tan 25 degrees
• tan 140 degrees

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 x-axis, 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 y-coordinate(0.9063) divided by the x-coordinate (0.4226). ∴ tan 65° = 2.1445