Tan 300 Degrees
The value of tan 300 degrees is -1.7320508. . .. Tan 300 degrees in radians is written as tan (300° × π/180°), i.e., tan (5π/3) or tan (5.235987. . .). In this article, we will discuss the methods to find the value of tan 300 degrees with examples.
- Tan 300°: -√3
- Tan 300° in decimal: -1.7320508. . .
- Tan (-300 degrees): 1.7320508. . . or √3
- Tan 300° in radians: tan (5π/3) or tan (5.2359877 . . .)
What is the Value of Tan 300 Degrees?
The value of tan 300 degrees in decimal is -1.732050807. . .. Tan 300 degrees can also be expressed using the equivalent of the given angle (300 degrees) in radians (5.23598 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 300 degrees = 300° × (π/180°) rad = 5π/3 or 5.2359 . . .
∴ tan 300° = tan(5.2359) = -√3 or -1.7320508. . .
Explanation:
For tan 300 degrees, the angle 300° lies between 270° and 360° (Fourth Quadrant). Since tangent function is negative in the fourth quadrant, thus tan 300° value = -√3 or -1.7320508. . .
Since the tangent function is a periodic function, we can represent tan 300° as, tan 300 degrees = tan(300° + n × 180°), n ∈ Z.
⇒ tan 300° = tan 480° = tan 660°, and so on.
Note: Since, tangent is an odd function, the value of tan(-300°) = -tan(300°).
Methods to Find Value of Tan 300 Degrees
The tangent function is negative in the 4th quadrant. The value of tan 300° is given as -1.73205. . .. We can find the value of tan 300 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 300° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 300 degrees as:
- sin(300°)/cos(300°)
- ± sin 300°/√(1 - sin²(300°))
- ± √(1 - cos²(300°))/cos 300°
- ± 1/√(cosec²(300°) - 1)
- ± √(sec²(300°) - 1)
- 1/cot 300°
Note: Since 300° lies in the 4th Quadrant, the final value of tan 300° will be negative.
We can use trigonometric identities to represent tan 300° as,
- cot(90° - 300°) = cot(-210°)
- -cot(90° + 300°) = -cot 390°
- -tan (180° - 300°) = -tan(-120°)
Tan 300 Degrees Using Unit Circle
To find the value of tan 300 degrees using the unit circle:
- Rotate ‘r’ anticlockwise to form 300° angle with the positive x-axis.
- The tan of 300 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 300° = y/x = -1.7321 (approx).
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FAQs on Tan 300 Degrees
What is Tan 300 Degrees?
Tan 300 degrees is the value of tangent trigonometric function for an angle equal to 300 degrees. The value of tan 300° is -√3 or -1.7321 (approx).
What is the Value of Tan 300° in Terms of Sec 300°?
We can represent the tangent function in terms of the secant function using trig identities, tan 300° can be written as -√(sec²(300°) - 1). Here, the value of sec 300° is equal to 2.
How to Find the Value of Tan 300 Degrees?
The value of tan 300 degrees can be calculated by constructing an angle of 300° 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 300° is equal to the y-coordinate(-0.866) divided by the x-coordinate (0.5). ∴ tan 300° = -√3 or -1.7321
What is the Value of Tan 300 Degrees in Terms of Cos 300°?
We know, using trig identities, we can write tan 300° as -√(1 - cos²(300°))/cos 300°. Here, the value of cos 300° is equal to 0.5.
How to Find Tan 300° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 300° can be given in terms of other trigonometric functions as:
- sin(300°)/cos(300°)
- ± sin 300°/√(1 - sin²(300°))
- ± √(1 - cos²(300°))/cos 300°
- ± 1/√(cosec²(300°) - 1)
- ± √(sec²(300°) - 1)
- 1/cot 300°
☛ Also check: trigonometric table