Tan 66 Degrees

The value of tan 66 degrees is 2.2460367. . .. Tan 66 degrees in radians is written as tan (66° × π/180°), i.e., tan (11π/30) or tan (1.151917. . .). In this article, we will discuss the methods to find the value of tan 66 degrees with examples.

• Tan 66° in decimal: 2.2460367. . .
• Tan (-66 degrees): -2.2460367. . .
• Tan 66° in radians: tan (11π/30) or tan (1.1519173 . . .)

What is the Value of Tan 66 Degrees?

The value of tan 66 degrees in decimal is 2.246036773. . .. Tan 66 degrees can also be expressed using the equivalent of the given angle (66 degrees) in radians (1.15191 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 66 degrees = 66° × (π/180°) rad = 11π/30 or 1.1519 . . .
∴ tan 66° = tan(1.1519) = 2.2460367. . .

Explanation:

For tan 66 degrees, the angle 66° lies between 0° and 90° (First Quadrant). Since tangent function is positive in the first quadrant, thus tan 66° value = 2.2460367. . .
Since the tangent function is a periodic function, we can represent tan 66° as, tan 66 degrees = tan(66° + n × 180°), n ∈ Z.
⇒ tan 66° = tan 246° = tan 426°, and so on.
Note: Since, tangent is an odd function, the value of tan(-66°) = -tan(66°).

Methods to Find Value of Tan 66 Degrees

The tangent function is positive in the 1st quadrant. The value of tan 66° is given as 2.24603. . .. We can find the value of tan 66 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Tan 66° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 66 degrees as:

• sin(66°)/cos(66°)
• ± sin 66°/√(1 - sin²(66°))
• ± √(1 - cos²(66°))/cos 66°
• ± 1/√(cosec²(66°) - 1)
• ± √(sec²(66°) - 1)
• 1/cot 66°

Note: Since 66° lies in the 1st Quadrant, the final value of tan 66° will be positive.

We can use trigonometric identities to represent tan 66° as,

• cot(90° - 66°) = cot 24°
• -cot(90° + 66°) = -cot 156°
• -tan (180° - 66°) = -tan 114°

Tan 66 Degrees Using Unit Circle

To find the value of tan 66 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 66° angle with the positive x-axis.
• The tan of 66 degrees equals the y-coordinate(0.9135) divided by x-coordinate(0.4067) of the point of intersection (0.4067, 0.9135) of unit circle and r.

Hence the value of tan 66° = y/x = 2.246 (approx).

☛ Also Check:

• tan 105 degrees
• tan 60 degrees
• tan 10 degrees
• tan 24 degrees
• tan 89 degrees
• tan 999 degrees

FAQs on Tan 66 Degrees

What is Tan 66 Degrees?

Tan 66 degrees is the value of tangent trigonometric function for an angle equal to 66 degrees. The value of tan 66° is 2.246 (approx).

What is the Exact Value of tan 66 Degrees?

The exact value of tan 66 degrees can be given accurately up to 8 decimal places as 2.24603677.

How to Find Tan 66° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 66° can be given in terms of other trigonometric functions as:

• sin(66°)/cos(66°)
• ± sin 66°/√(1 - sin²(66°))
• ± √(1 - cos²(66°))/cos 66°
• ± 1/√(cosec²(66°) - 1)
• ± √(sec²(66°) - 1)
• 1/cot 66°

☛ Also check: trigonometry table

What is the Value of Tan 66 Degrees in Terms of Sin 66°?

Using trigonometric identities, we can write tan 66° in terms of sin 66° as, tan(66°) = sin 66°/√(1 - sin²(66°)) . Here, the value of sin 66° is equal to 0.9135.

How to Find the Value of Tan 66 Degrees?

The value of tan 66 degrees can be calculated by constructing an angle of 66° with the x-axis, and then finding the coordinates of the corresponding point (0.4067, 0.9135) on the unit circle. The value of tan 66° is equal to the y-coordinate(0.9135) divided by the x-coordinate (0.4067). ∴ tan 66° = 2.246