Tan 999 Degrees
The value of tan 999 degrees is -6.3137515. . .. Tan 999 degrees in radians is written as tan (999° × π/180°), i.e., tan (111π/20) or tan (17.435839. . .). In this article, we will discuss the methods to find the value of tan 999 degrees with examples.
- Tan 999° in decimal: -6.3137515. . .
- Tan (-999 degrees): 6.3137515. . .
- Tan 999° in radians: tan (111π/20) or tan (17.4358392 . . .)
What is the Value of Tan 999 Degrees?
The value of tan 999 degrees in decimal is -6.313751514. . .. Tan 999 degrees can also be expressed using the equivalent of the given angle (999 degrees) in radians (17.43583 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 999 degrees = 999° × (π/180°) rad = 111π/20 or 17.4358 . . .
∴ tan 999° = tan(17.4358) = -6.3137515. . .
Explanation:
For tan 999°, the angle 999° > 360°. We can represent tan 999° as, tan(999° mod 360°) = tan(279°). The angle 999°, coterminal to angle 279°, is located in the Fourth Quadrant(Quadrant IV).
Since tangent function is negative in the 4th quadrant, thus tan 999 degrees value = -6.3137515. . .
Similarly, given the periodic property of tan 999°, it can also be written as, tan 999 degrees = (999° + n × 180°), n ∈ Z.
⇒ tan 999° = tan 1179° = tan 1359°, and so on.
Note: Since, tangent is an odd function, the value of tan(-999°) = -tan(999°).
Methods to Find Value of Tan 999 Degrees
The tangent function is negative in the 4th quadrant. The value of tan 999° is given as -6.31375. . .. We can find the value of tan 999 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Tan 999 Degrees Using Unit Circle
To find the value of tan 999 degrees using the unit circle, represent 999° in the form (2 × 360°) + 279° [∵ 999°>360°] ∵ The angle 999° is coterminal to 279° angle and also tangent is a periodic function, tan 999° = tan 279°.
- Rotate ‘r’ anticlockwise to form 279° or 999° angle with the positive x-axis.
- The tan of 999 degrees equals the y-coordinate(-0.9877) divided by x-coordinate(0.1564) of the point of intersection (0.1564, -0.9877) of unit circle and r.
Hence the value of tan 999° = y/x = -6.3138 (approx).
Tan 999° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 999 degrees as:
- sin(999°)/cos(999°)
- ± sin 999°/√(1 - sin²(999°))
- ± √(1 - cos²(999°))/cos 999°
- ± 1/√(cosec²(999°) - 1)
- ± √(sec²(999°) - 1)
- 1/cot 999°
Note: Since 999° lies in the 4th Quadrant, the final value of tan 999° will be negative.
We can use trigonometric identities to represent tan 999° as,
- cot(90° - 999°) = cot(-909°)
- -cot(90° + 999°) = -cot 1089°
- -tan (180° - 999°) = -tan(-819°)
☛ Also Check:
FAQs on Tan 999 Degrees
What is Tan 999 Degrees?
Tan 999 degrees is the value of tangent trigonometric function for an angle equal to 999 degrees. The value of tan 999° is -6.3138 (approx).
How to Find Tan 999° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 999° can be given in terms of other trigonometric functions as:
- sin(999°)/cos(999°)
- ± sin 999°/√(1 - sin²(999°))
- ± √(1 - cos²(999°))/cos 999°
- ± 1/√(cosec²(999°) - 1)
- ± √(sec²(999°) - 1)
- 1/cot 999°
☛ Also check: trigonometric table
What is the Value of Tan 999° in Terms of Sec 999°?
We can represent the tangent function in terms of the secant function using trig identities, tan 999° can be written as -√(sec²(999°) - 1). Here, the value of sec 999° is equal to 6.3924.
How to Find the Value of Tan 999 Degrees?
The value of tan 999 degrees can be calculated by constructing an angle of 999° with the x-axis, and then finding the coordinates of the corresponding point (0.1564, -0.9877) on the unit circle. The value of tan 999° is equal to the y-coordinate(-0.9877) divided by the x-coordinate (0.1564). ∴ tan 999° = -6.3138
What is the Value of Tan 999 Degrees in Terms of Sin 999°?
Using trigonometric identities, we can write tan 999° in terms of sin 999° as, tan(999°) = sin 999°/√(1 - sin²(999°)) . Here, the value of sin 999° is equal to -0.9877.