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Sec 15 Degrees
The value of Sec 15 degrees is 1.0352761. . .. Sec 15 degrees in radians is written as sec (15° × π/180°), i.e., sec (π/12) or sec (0.261799. . .). In this article, we will discuss the methods to find the value of sec 15 degrees with examples.
 Sec 15°: √6  √2
 Sec 15° in decimal: 1.0352761. . .
 Sec (15 degrees): 1.0352761. . . or √6  √2
 Sec 15° in radians: sec (π/12) or sec (0.2617993 . . .)
What is the Value of Sec 15 Degrees?
The value of sec 15 degrees in decimal is 1.035276180. . .. Sec 15 degrees can also be expressed using the equivalent of the given angle (15 degrees) in radians (0.26179 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 15 degrees = 15° × (π/180°) rad = π/12 or 0.2617 . . .
∴ sec 15° = sec(0.2617) = √6  √2 or 1.0352761. . .
Explanation:
For sec 15 degrees, the angle 15° lies between 0° and 90° (First Quadrant). Since secant function is positive in the first quadrant, thus sec 15° value = √6  √2 or 1.0352761. . .
Since the secant function is a periodic function, we can represent sec 15° as, sec 15 degrees = sec(15° + n × 360°), n ∈ Z.
⇒ sec 15° = sec 375° = sec 735°, and so on.
Note: Since, secant is an even function, the value of sec(15°) = sec(15°).
Methods to Find Value of Sec 15 Degrees
The secant function is positive in the 1st quadrant. The value of sec 15° is given as 1.03527. . .. We can find the value of sec 15 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sec 15° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec 15 degrees as:
 ± 1/√(1  sin²(15°))
 ± √(1 + tan²(15°))
 ± √(1 + cot²(15°))/cot 15°
 ± cosec 15°/√(cosec²(15°)  1)
 1/cos 15°
Note: Since 15° lies in the 1st Quadrant, the final value of sec 15° will be positive.
We can use trigonometric identities to represent sec 15° as,
 sec(180°  15°) = sec 165°
 sec(180° + 15°) = sec 195°
 cosec(90° + 15°) = cosec 105°
 cosec(90°  15°) = cosec 75°
Sec 15 Degrees Using Unit Circle
To find the value of sec 15 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 15° angle with the positive xaxis.
 The sec of 15 degrees equals the reciprocal of the xcoordinate(0.9659) of the point of intersection (0.9659, 0.2588) of unit circle and r.
Hence the value of sec 15° = 1/x = 1.0353 (approx)
☛ Also Check:
Examples Using Sec 15 Degrees

Example 1: Find the value of sec 15° if cos 15° is 0.9659.
Solution:
Since, sec 15° = 1/cos 15°
⇒ sec 15° = 1/0.9659 = 1.0353 
Example 2: Simplify: 7 (sec 15°/cosec 105°)
Solution:
We know sec 15° = cosec 105°
⇒ 7 sec 15°/cosec 105° = 7 (sec 15°/sec 15°)
= 7(1) = 7 
Example 3: Find the value of 1/(cos² 7.5°  sin² 7.5°). [Hint: Use sec 15° = 1.0353]
Solution:
Using the cos 2a formula,
1/(cos² 7.5°  sin² 7.5°) = 1/cos(2 × 7.5°) = sec 15°
∵ sec 15° = 1.0353
⇒ 1/(cos² 7.5°  sin² 7.5°) = 1.0353
FAQs on Sec 15 Degrees
What is Sec 15 Degrees?
Sec 15 degrees is the value of secant trigonometric function for an angle equal to 15 degrees. The value of sec 15° is √6  √2 or 1.0353 (approx).
What is the Value of Sec 15 Degrees in Terms of Sin 15°?
Using trigonometric identities, we can write sec 15° in terms of sin 15° as, sec(15°) = 1/√(1  sin²(15°)). Here, the value of sin 15° is equal to 0.2588.
What is the Value of Sec 15° in Terms of Cos 15°?
Since the cosine function is the reciprocal of the secant function, we can write sec 15° as 1/cos(15°). The value of cos 15° is equal to 0.9659.
How to Find the Value of Sec 15 Degrees?
The value of sec 15 degrees can be calculated by constructing an angle of 15° with the xaxis, and then finding the coordinates of the corresponding point (0.9659, 0.2588) on the unit circle. The value of sec 15° is equal to the reciprocal of the xcoordinate(0.9659). ∴ sec 15° = 1.0353.
How to Find Sec 15° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec 15° can be given in terms of other trigonometric functions as:
 ± 1/√(1sin²(15°))
 ± √(1 + tan²(15°))
 ± √(1 + cot²(15°))/cot 15°
 ± cosec 15°/√(cosec²(15°)  1)
 1/cos 15°
☛ Also check: trigonometric table
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