Tan 510 Degrees
The value of tan 510 degrees is -0.5773502. . .. Tan 510 degrees in radians is written as tan (510° × π/180°), i.e., tan (17π/6) or tan (8.901179. . .). In this article, we will discuss the methods to find the value of tan 510 degrees with examples.
- Tan 510°: -1/√3
- Tan 510° in decimal: -0.5773502. . .
- Tan (-510 degrees): 0.5773502. . . or 1/√3
- Tan 510° in radians: tan (17π/6) or tan (8.9011791 . . .)
What is the Value of Tan 510 Degrees?
The value of tan 510 degrees in decimal is -0.577350269. . .. Tan 510 degrees can also be expressed using the equivalent of the given angle (510 degrees) in radians (8.90117 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 510 degrees = 510° × (π/180°) rad = 17π/6 or 8.9011 . . .
∴ tan 510° = tan(8.9011) = -1/√3 or -0.5773502. . .
Explanation:
For tan 510°, the angle 510° > 360°. We can represent tan 510° as, tan(510° mod 360°) = tan(150°). The angle 510°, coterminal to angle 150°, is located in the Second Quadrant(Quadrant II).
Since tangent function is negative in the 2nd quadrant, thus tan 510 degrees value = -1/√3 or -0.5773502. . .
Similarly, given the periodic property of tan 510°, it can also be written as, tan 510 degrees = (510° + n × 180°), n ∈ Z.
⇒ tan 510° = tan 690° = tan 870°, and so on.
Note: Since, tangent is an odd function, the value of tan(-510°) = -tan(510°).
Methods to Find Value of Tan 510 Degrees
The tangent function is negative in the 2nd quadrant. The value of tan 510° is given as -0.57735. . .. We can find the value of tan 510 degrees by:
- Using Trigonometric Functions
- Using Unit Circle
Tan 510° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the tan 510 degrees as:
- sin(510°)/cos(510°)
- ± sin 510°/√(1 - sin²(510°))
- ± √(1 - cos²(510°))/cos 510°
- ± 1/√(cosec²(510°) - 1)
- ± √(sec²(510°) - 1)
- 1/cot 510°
Note: Since 510° lies in the 2nd Quadrant, the final value of tan 510° will be negative.
We can use trigonometric identities to represent tan 510° as,
- cot(90° - 510°) = cot(-420°)
- -cot(90° + 510°) = -cot 600°
- -tan (180° - 510°) = -tan(-330°)
Tan 510 Degrees Using Unit Circle
To find the value of tan 510 degrees using the unit circle, represent 510° in the form (1 × 360°) + 150° [∵ 510°>360°] ∵ The angle 510° is coterminal to 150° angle and also tangent is a periodic function, tan 510° = tan 150°.
- Rotate ‘r’ anticlockwise to form 150° or 510° angle with the positive x-axis.
- The tan of 510 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 510° = y/x = -0.5774 (approx).
☛ Also Check:
FAQs on Tan 510 Degrees
What is Tan 510 Degrees?
Tan 510 degrees is the value of tangent trigonometric function for an angle equal to 510 degrees. The value of tan 510° is -1/√3 or -0.5774 (approx).
How to Find the Value of Tan 510 Degrees?
The value of tan 510 degrees can be calculated by constructing an angle of 510° 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 510° is equal to the y-coordinate(0.5) divided by the x-coordinate (-0.866). ∴ tan 510° = -1/√3 or -0.5774
What is the Value of Tan 510 Degrees in Terms of Cos 510°?
We know, using trig identities, we can write tan 510° as √(1 - cos²(510°))/cos 510°. Here, the value of cos 510° is equal to -0.866025.
What is the Exact Value of tan 510 Degrees?
The exact value of tan 510 degrees can be given accurately up to 8 decimal places as -0.57735026 or as -1/√3.
How to Find Tan 510° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of tan 510° can be given in terms of other trigonometric functions as:
- sin(510°)/cos(510°)
- ± sin 510°/√(1 - sin²(510°))
- ± √(1 - cos²(510°))/cos 510°
- ± 1/√(cosec²(510°) - 1)
- ± √(sec²(510°) - 1)
- 1/cot 510°
☛ Also check: trigonometric table