Sec 11 Degrees
The value of Sec 11 degrees is 1.0187166. . .. Sec 11 degrees in radians is written as sec (11° × π/180°), i.e., sec (0.191986. . .). In this article, we will discuss the methods to find the value of sec 11 degrees with examples.
 Sec 11° in decimal: 1.0187166. . .
 Sec (11 degrees): 1.0187166. . .
 Sec 11° in radians: sec (0.1919862 . . .)
What is the Value of Sec 11 Degrees?
The value of sec 11 degrees in decimal is 1.018716694. . .. Sec 11 degrees can also be expressed using the equivalent of the given angle (11 degrees) in radians (0.19198 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 11 degrees = 11° × (π/180°) rad = 0.1919 . . .
∴ sec 11° = sec(0.1919) = 1.0187166. . .
Explanation:
For sec 11 degrees, the angle 11° lies between 0° and 90° (First Quadrant). Since secant function is positive in the first quadrant, thus sec 11° value = 1.0187166. . .
Since the secant function is a periodic function, we can represent sec 11° as, sec 11 degrees = sec(11° + n × 360°), n ∈ Z.
⇒ sec 11° = sec 371° = sec 731°, and so on.
Note: Since, secant is an even function, the value of sec(11°) = sec(11°).
Methods to Find Value of Sec 11 Degrees
The secant function is positive in the 1st quadrant. The value of sec 11° is given as 1.01871. . .. We can find the value of sec 11 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sec 11° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec 11 degrees as:
 ± 1/√(1  sin²(11°))
 ± √(1 + tan²(11°))
 ± √(1 + cot²(11°))/cot 11°
 ± cosec 11°/√(cosec²(11°)  1)
 1/cos 11°
Note: Since 11° lies in the 1st Quadrant, the final value of sec 11° will be positive.
We can use trigonometric identities to represent sec 11° as,
 sec(180°  11°) = sec 169°
 sec(180° + 11°) = sec 191°
 cosec(90° + 11°) = cosec 101°
 cosec(90°  11°) = cosec 79°
Sec 11 Degrees Using Unit Circle
To find the value of sec 11 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 11° angle with the positive xaxis.
 The sec of 11 degrees equals the reciprocal of the xcoordinate(0.9816) of the point of intersection (0.9816, 0.1908) of unit circle and r.
Hence the value of sec 11° = 1/x = 1.0187 (approx)
☛ Also Check:
Examples Using Sec 11 Degrees

Example 1: Using the value of sec 11°, solve: (1 + tan²(11°)).
Solution:
We know, (1 + tan²(11°)) = (sec²(11°)) = 1.0378
⇒ (1 + tan²(11°)) = 1.0378 
Example 2: Find the value of 1/(cos² 5.5°  sin² 5.5°). [Hint: Use sec 11° = 1.0187]
Solution:
Using the cos 2a formula,
1/(cos² 5.5°  sin² 5.5°) = 1/cos(2 × 5.5°) = sec 11°
∵ sec 11° = 1.0187
⇒ 1/(cos² 5.5°  sin² 5.5°) = 1.0187 
Example 3: Find the value of sec 11° if cos 11° is 0.9816.
Solution:
Since, sec 11° = 1/cos 11°
⇒ sec 11° = 1/0.9816 = 1.0187
FAQs on Sec 11 Degrees
What is Sec 11 Degrees?
Sec 11 degrees is the value of secant trigonometric function for an angle equal to 11 degrees. The value of sec 11° is 1.0187 (approx).
How to Find Sec 11° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec 11° can be given in terms of other trigonometric functions as:
 ± 1/√(1sin²(11°))
 ± √(1 + tan²(11°))
 ± √(1 + cot²(11°))/cot 11°
 ± cosec 11°/√(cosec²(11°)  1)
 1/cos 11°
☛ Also check: trigonometric table
What is the Value of Sec 11 Degrees in Terms of Sin 11°?
Using trigonometric identities, we can write sec 11° in terms of sin 11° as, sec(11°) = 1/√(1  sin²(11°)). Here, the value of sin 11° is equal to 0.1908.
How to Find the Value of Sec 11 Degrees?
The value of sec 11 degrees can be calculated by constructing an angle of 11° with the xaxis, and then finding the coordinates of the corresponding point (0.9816, 0.1908) on the unit circle. The value of sec 11° is equal to the reciprocal of the xcoordinate(0.9816). ∴ sec 11° = 1.0187.
What is the Value of Sec 11° in Terms of Cosec 11°?
Since the secant function can be represented using the cosecant function, we can write sec 11° as [cosec 11°/√(cosec²(11°)  1)]. The value of cosec 11° is equal to 5.2408.
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