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Tan 330 Degrees

The value of tan 330 degrees is -0.5773502. . .. Tan 330 degrees in radians is written as tan (330° × π/180°), i.e., tan (11π/6) or tan (5.759586. . .). In this article, we will discuss the methods to find the value of tan 330 degrees with examples.

Tan 330°: -1/√3
Tan 330° in decimal: -0.5773502. . .
Tan (-330 degrees): 0.5773502. . . or 1/√3
Tan 330° in radians: tan (11π/6) or tan (5.7595865 . . .)

What is the Value of Tan 330 Degrees?

The value of tan 330 degrees in decimal is -0.577350269. . .. Tan 330 degrees can also be expressed using the equivalent of the given angle (330 degrees) in radians (5.75958 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 330 degrees = 330° × (π/180°) rad = 11π/6 or 5.7595 . . .
∴ tan 330° = tan(5.7595) = -1/√3 or -0.5773502. . .

Explanation:

For tan 330 degrees, the angle 330° lies between 270° and 360° (Fourth Quadrant). Since tangent function is negative in the fourth quadrant, thus tan 330° value = -1/√3 or -0.5773502. . .
Since the tangent function is a periodic function, we can represent tan 330° as, tan 330 degrees = tan(330° + n × 180°), n ∈ Z.
⇒ tan 330° = tan 510° = tan 690°, and so on.
Note: Since, tangent is an odd function, the value of tan(-330°) = -tan(330°).

Methods to Find Value of Tan 330 Degrees

The tangent function is negative in the 4th quadrant. The value of tan 330° is given as -0.57735. . .. We can find the value of tan 330 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 330° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 330 degrees as:

sin(330°)/cos(330°)
± sin 330°/√(1 - sin²(330°))
± √(1 - cos²(330°))/cos 330°
± 1/√(cosec²(330°) - 1)
± √(sec²(330°) - 1)
1/cot 330°

Note: Since 330° lies in the 4th Quadrant, the final value of tan 330° will be negative.

We can use trigonometric identities to represent tan 330° as,

cot(90° - 330°) = cot(-240°)
-cot(90° + 330°) = -cot 420°
-tan (180° - 330°) = -tan(-150°)

Tan 330 Degrees Using Unit Circle

To find the value of tan 330 degrees using the unit circle:

Rotate ‘r’ anticlockwise to form 330° angle with the positive x-axis.
The tan of 330 degrees equals the y-coordinate(-0.5) divided by x-coordinate(0.866) of the point of intersection (0.866, -0.5) of unit circle and r.

Hence the value of tan 330° = y/x = -0.5774 (approx).

☛ Also Check:

Examples Using Tan 330 Degrees

Example 1: Using the value of tan 330°, solve: (sec²(330°) - 1).

Solution:
We know, (sec²(330°) - 1) = (tan²(330°)) = 0.3333
⇒ (sec²(330°) - 1) = 0.3333
Example 2: Find the value of 7 tan(330°)/10 tan(-150°).

Solution:

Using trigonometric identities, we know, tan(330°) = -tan(180° - 330°) = -tan(-150°).
⇒ tan(330°) = -tan(-150°)
⇒ Value of 7 tan(330°)/10 tan(-150°) = -7/10
Example 3: Find the value of (2 sin (165°) cos (165°) sec (330°)). [Hint: Use tan 330° = -0.5774]

Solution:

Using sin 2a formula,
2 sin (165°) cos (165°) = sin (2 × 165°) = sin 330°
⇒ 2 sin (165°) cos (165°) sec(330°) = sin 330° sec 330°
= sin 330°/cos 330° = tan 330°
⇒ (2 sin (165°) cos (165°) sec(330°)) = -0.5774

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FAQs on Tan 330 Degrees

What is Tan 330 Degrees?

Tan 330 degrees is the value of tangent trigonometric function for an angle equal to 330 degrees. The value of tan 330° is -1/√3 or -0.5774 (approx).

How to Find the Value of Tan 330 Degrees?

The value of tan 330 degrees can be calculated by constructing an angle of 330° with the x-axis, and then finding the coordinates of the corresponding point (0.866, -0.5) on the unit circle. The value of tan 330° is equal to the y-coordinate(-0.5) divided by the x-coordinate (0.866). ∴ tan 330° = -1/√3 or -0.5774

What is the Value of Tan 330 Degrees in Terms of Cot 330°?

Since the tangent function is the reciprocal of the cotangent function, we can write tan 330° as 1/cot(330°). The value of cot 330° is equal to -√3.

What is the Value of Tan 330° in Terms of Cosec 330°?

Since the tangent function can be represented using the cosecant function, we can write tan 330° as -1/√(cosec²(330°) - 1). The value of cosec 330° is equal to -2.

How to Find Tan 330° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 330° can be given in terms of other trigonometric functions as:

sin(330°)/cos(330°)
± sin 330°/√(1 - sin²(330°))
± √(1 - cos²(330°))/cos 330°
± 1/√(cosec²(330°) - 1)
± √(sec²(330°) - 1)
1/cot 330°

☛ Also check: trigonometry table

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