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Tan 600 Degrees

The value of tan 600 degrees is 1.7320508. . .. Tan 600 degrees in radians is written as tan (600° × π/180°), i.e., tan (10π/3) or tan (10.471975. . .). In this article, we will discuss the methods to find the value of tan 600 degrees with examples.

Tan 600°: √3
Tan 600° in decimal: 1.7320508. . .
Tan (-600 degrees): -1.7320508. . . or -√3
Tan 600° in radians: tan (10π/3) or tan (10.4719755 . . .)

What is the Value of Tan 600 Degrees?

The value of tan 600 degrees in decimal is 1.732050807. . .. Tan 600 degrees can also be expressed using the equivalent of the given angle (600 degrees) in radians (10.47197 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 600 degrees = 600° × (π/180°) rad = 10π/3 or 10.4719 . . .
∴ tan 600° = tan(10.4719) = √3 or 1.7320508. . .

Explanation:

For tan 600°, the angle 600° > 360°. We can represent tan 600° as, tan(600° mod 360°) = tan(240°). The angle 600°, coterminal to angle 240°, is located in the Third Quadrant(Quadrant III).
Since tangent function is positive in the 3rd quadrant, thus tan 600 degrees value = √3 or 1.7320508. . .
Similarly, given the periodic property of tan 600°, it can also be written as, tan 600 degrees = (600° + n × 180°), n ∈ Z.
⇒ tan 600° = tan 780° = tan 960°, and so on.
Note: Since, tangent is an odd function, the value of tan(-600°) = -tan(600°).

Methods to Find Value of Tan 600 Degrees

The tangent function is positive in the 3rd quadrant. The value of tan 600° is given as 1.73205. . .. We can find the value of tan 600 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 600° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 600 degrees as:

sin(600°)/cos(600°)
± sin 600°/√(1 - sin²(600°))
± √(1 - cos²(600°))/cos 600°
± 1/√(cosec²(600°) - 1)
± √(sec²(600°) - 1)
1/cot 600°

Note: Since 600° lies in the 3rd Quadrant, the final value of tan 600° will be positive.

We can use trigonometric identities to represent tan 600° as,

cot(90° - 600°) = cot(-510°)
-cot(90° + 600°) = -cot 690°
-tan (180° - 600°) = -tan(-420°)

Tan 600 Degrees Using Unit Circle

To find the value of tan 600 degrees using the unit circle, represent 600° in the form (1 × 360°) + 240° [∵ 600°>360°] ∵ The angle 600° is coterminal to 240° angle and also tangent is a periodic function, tan 600° = tan 240°.

Rotate ‘r’ anticlockwise to form 240° or 600° angle with the positive x-axis.
The tan of 600 degrees equals the y-coordinate(-0.866) divided by x-coordinate(-0.5) of the point of intersection (-0.5, -0.866) of unit circle and r.

Hence the value of tan 600° = y/x = 1.7321 (approx).

☛ Also Check:

Examples Using Tan 600 Degrees

Example 1: Using the value of tan 600°, solve: (sec²(600°) - 1).

Solution:
We know, (sec²(600°) - 1) = (tan²(600°)) = 3
⇒ (sec²(600°) - 1) = 3
Example 2: Find the value of (2 sin (300°) cos (300°) sec (600°)). [Hint: Use tan 600° = 1.7321]

Solution:

Using sin 2a formula,
2 sin (300°) cos (300°) = sin (2 × 300°) = sin 600°
⇒ 2 sin (300°) cos (300°) sec(600°) = sin 600° sec 600°
= sin 600°/cos 600° = tan 600°
⇒ (2 sin (300°) cos (300°) sec(600°)) = 1.7321
Example 3: Find the value of 2 tan(600°)/6 tan(-420°).

Solution:

Using trigonometric identities, we know, tan(600°) = -tan(180° - 600°) = -tan(-420°).
⇒ tan(600°) = -tan(-420°)
⇒ Value of 2 tan(600°)/6 tan(-420°) = -2/6 = -1/3

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FAQs on Tan 600 Degrees

What is Tan 600 Degrees?

Tan 600 degrees is the value of tangent trigonometric function for an angle equal to 600 degrees. The value of tan 600° is √3 or 1.7321 (approx).

What is the Value of Tan 600 Degrees in Terms of Sin 600°?

Using trigonometric identities, we can write tan 600° in terms of sin 600° as, tan(600°) = -sin 600°/√(1 - sin²(600°)) . Here, the value of sin 600° is equal to -0.866.

What is the Exact Value of tan 600 Degrees?

The exact value of tan 600 degrees can be given accurately up to 8 decimal places as 1.73205080 or as √3.

How to Find the Value of Tan 600 Degrees?

The value of tan 600 degrees can be calculated by constructing an angle of 600° with the x-axis, and then finding the coordinates of the corresponding point (-0.5, -0.866) on the unit circle. The value of tan 600° is equal to the y-coordinate(-0.866) divided by the x-coordinate (-0.5). ∴ tan 600° = √3 or 1.7321

How to Find Tan 600° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 600° can be given in terms of other trigonometric functions as:

sin(600°)/cos(600°)
± sin 600°/√(1 - sin²(600°))
± √(1 - cos²(600°))/cos 600°
± 1/√(cosec²(600°) - 1)
± √(sec²(600°) - 1)
1/cot 600°

☛ Also check: trigonometric table

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