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Tan 499 Degrees

The value of tan 499 degrees is -0.8692867. . .. Tan 499 degrees in radians is written as tan (499° × π/180°), i.e., tan (8.709192. . .). In this article, we will discuss the methods to find the value of tan 499 degrees with examples.

Tan 499° in decimal: -0.8692867. . .
Tan (-499 degrees): 0.8692867. . .
Tan 499° in radians: tan (8.7091929 . . .)

What is the Value of Tan 499 Degrees?

The value of tan 499 degrees in decimal is -0.869286737. . .. Tan 499 degrees can also be expressed using the equivalent of the given angle (499 degrees) in radians (8.70919 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 499 degrees = 499° × (π/180°) rad = 8.7091 . . .
∴ tan 499° = tan(8.7091) = -0.8692867. . .

Explanation:

For tan 499°, the angle 499° > 360°. We can represent tan 499° as, tan(499° mod 360°) = tan(139°). The angle 499°, coterminal to angle 139°, is located in the Second Quadrant(Quadrant II).
Since tangent function is negative in the 2nd quadrant, thus tan 499 degrees value = -0.8692867. . .
Similarly, given the periodic property of tan 499°, it can also be written as, tan 499 degrees = (499° + n × 180°), n ∈ Z.
⇒ tan 499° = tan 679° = tan 859°, and so on.
Note: Since, tangent is an odd function, the value of tan(-499°) = -tan(499°).

Methods to Find Value of Tan 499 Degrees

The tangent function is negative in the 2nd quadrant. The value of tan 499° is given as -0.86928. . .. We can find the value of tan 499 degrees by:

Using Trigonometric Functions
Using Unit Circle

Tan 499° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the tan 499 degrees as:

sin(499°)/cos(499°)
± sin 499°/√(1 - sin²(499°))
± √(1 - cos²(499°))/cos 499°
± 1/√(cosec²(499°) - 1)
± √(sec²(499°) - 1)
1/cot 499°

Note: Since 499° lies in the 2nd Quadrant, the final value of tan 499° will be negative.

We can use trigonometric identities to represent tan 499° as,

cot(90° - 499°) = cot(-409°)
-cot(90° + 499°) = -cot 589°
-tan (180° - 499°) = -tan(-319°)

Tan 499 Degrees Using Unit Circle

To find the value of tan 499 degrees using the unit circle, represent 499° in the form (1 × 360°) + 139° [∵ 499°>360°] ∵ The angle 499° is coterminal to 139° angle and also tangent is a periodic function, tan 499° = tan 139°.

Rotate ‘r’ anticlockwise to form 139° or 499° angle with the positive x-axis.
The tan of 499 degrees equals the y-coordinate(0.6561) divided by x-coordinate(-0.7547) of the point of intersection (-0.7547, 0.6561) of unit circle and r.

Hence the value of tan 499° = y/x = -0.8693 (approx).

☛ Also Check:

Examples Using Tan 499 Degrees

Example 1: Find the value of 6 tan(499°)/9 tan(-319°).

Solution:

Using trigonometric identities, we know, tan(499°) = -tan(180° - 499°) = -tan(-319°).
⇒ tan(499°) = -tan(-319°)
⇒ Value of 6 tan(499°)/9 tan(-319°) = -6/9 = -2/3
Example 2: Find the value of tan 499° if cot 499° is -1.1503.

Solution:
Since, tan 499° = 1/cot 499°
⇒ tan 499° = 1/(-1.1503) = -0.8693
Example 3: Find the value of (2 sin (249.5°) cos (249.5°) sec (499°)). [Hint: Use tan 499° = -0.8693]

Solution:

Using sin 2a formula,
2 sin (249.5°) cos (249.5°) = sin (2 × 249.5°) = sin 499°
⇒ 2 sin (249.5°) cos (249.5°) sec(499°) = sin 499° sec 499°
= sin 499°/cos 499° = tan 499°
⇒ (2 sin (249.5°) cos (249.5°) sec(499°)) = -0.8693

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FAQs on Tan 499 Degrees

What is Tan 499 Degrees?

Tan 499 degrees is the value of tangent trigonometric function for an angle equal to 499 degrees. The value of tan 499° is -0.8693 (approx).

How to Find Tan 499° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of tan 499° can be given in terms of other trigonometric functions as:

sin(499°)/cos(499°)
± sin 499°/√(1 - sin²(499°))
± √(1 - cos²(499°))/cos 499°
± 1/√(cosec²(499°) - 1)
± √(sec²(499°) - 1)
1/cot 499°

☛ Also check: trigonometric table

What is the Exact Value of tan 499 Degrees?

The exact value of tan 499 degrees can be given accurately up to 8 decimal places as -0.86928673.

How to Find the Value of Tan 499 Degrees?

The value of tan 499 degrees can be calculated by constructing an angle of 499° with the x-axis, and then finding the coordinates of the corresponding point (-0.7547, 0.6561) on the unit circle. The value of tan 499° is equal to the y-coordinate(0.6561) divided by the x-coordinate (-0.7547). ∴ tan 499° = -0.8693

What is the Value of Tan 499 Degrees in Terms of Cos 499°?

We know, using trig identities, we can write tan 499° as √(1 - cos²(499°))/cos 499°. Here, the value of cos 499° is equal to -0.754709.

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