Sec 510 Degrees
The value of Sec 510 degrees is -1.1547005. . .. Sec 510 degrees in radians is written as sec (510° × π/180°), i.e., sec (17π/6) or sec (8.901179. . .). In this article, we will discuss the methods to find the value of sec 510 degrees with examples.
- Sec 510°: -2/√3
- Sec 510° in decimal: -1.1547005. . .
- Sec (-510 degrees): -1.1547005. . . or -2/√3
- Sec 510° in radians: sec (17π/6) or sec (8.9011791 . . .)
What is the Value of Sec 510 Degrees?
The value of sec 510 degrees in decimal is -1.154700538. . .. Sec 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 . . .
∴ sec 510° = sec(8.9011) = -2/√3 or -1.1547005. . .
Explanation:
For sec 510°, the angle 510° > 360°. Given the periodic property of the secant function, we can represent it as sec(510° mod 360°) = sec(150°). The angle 510°, coterminal to angle 150°, is located in the Second Quadrant(Quadrant II).
Since secant function is negative in the 2nd quadrant, thus sec 510 degrees value = -2/√3 or -1.1547005. . .
Similarly, sec 510° can also be written as, sec 510 degrees = (510° + n × 360°), n ∈ Z.
⇒ sec 510° = sec 870° = sec 1230°, and so on.
Note: Since, secant is an even function, the value of sec(-510°) = sec(510°).
Methods to Find Value of Sec 510 Degrees
The secant function is negative in the 2nd quadrant. The value of sec 510° is given as -1.15470. . .. We can find the value of sec 510 degrees by:
- Using Unit Circle
- Using Trigonometric Functions
Sec 510 Degrees Using Unit Circle
To find the value of sec 510 degrees using the unit circle, represent 510° in the form (1 × 360°) + 150° [∵ 510°>360°] ∵ secant is a periodic function, sec 510° = sec 150°.
- Rotate ‘r’ anticlockwise to form 150° or 510° angle with the positive x-axis.
- The sec of 510 degrees equals the reciprocal of the x-coordinate(-0.866) of the point of intersection (-0.866, 0.5) of unit circle and r.
Hence the value of sec 510° = 1/x = -1.1547 (approx)
Sec 510° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec 510 degrees as:
- ± 1/√(1 - sin²(510°))
- ± √(1 + tan²(510°))
- ± √(1 + cot²(510°))/cot 510°
- ± cosec 510°/√(cosec²(510°) - 1)
- 1/cos 510°
Note: Since 510° lies in the 2nd Quadrant, the final value of sec 510° will be negative.
We can use trigonometric identities to represent sec 510° as,
- -sec(180° - 510°) = -sec(-330°)
- -sec(180° + 510°) = -sec 690°
- cosec(90° + 510°) = cosec 600°
- cosec(90° - 510°) = cosec(-420°)
☛ Also Check:
FAQs on Sec 510 Degrees
What is Sec 510 Degrees?
Sec 510 degrees is the value of secant trigonometric function for an angle equal to 510 degrees. The value of sec 510° is -2/√3 or -1.1547 (approx).
What is the Value of Sec 510° in Terms of Cos 510°?
Since the cosine function is the reciprocal of the secant function, we can write sec 510° as 1/cos(510°). The value of cos 510° is equal to -0.866.
How to Find the Value of Sec 510 Degrees?
The value of sec 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 sec 510° is equal to the reciprocal of the x-coordinate(-0.866). ∴ sec 510° = -1.1547.
How to Find Sec 510° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec 510° can be given in terms of other trigonometric functions as:
- ± 1/√(1-sin²(510°))
- ± √(1 + tan²(510°))
- ± √(1 + cot²(510°))/cot 510°
- ± cosec 510°/√(cosec²(510°) - 1)
- 1/cos 510°
☛ Also check: trigonometry table
What is the Value of Sec 510 Degrees in Terms of Sin 510°?
Using trigonometric identities, we can write sec 510° in terms of sin 510° as, sec(510°) = -1/√(1 - sin²(510°)). Here, the value of sin 510° is equal to 0.5.