Sec 28 Degrees
The value of Sec 28 degrees is 1.1325700. . .. Sec 28 degrees in radians is written as sec (28° × π/180°), i.e., sec (7π/45) or sec (0.488692. . .). In this article, we will discuss the methods to find the value of sec 28 degrees with examples.
 Sec 28° in decimal: 1.1325700. . .
 Sec (28 degrees): 1.1325700. . .
 Sec 28° in radians: sec (7π/45) or sec (0.4886921 . . .)
What is the Value of Sec 28 Degrees?
The value of sec 28 degrees in decimal is 1.132570050. . .. Sec 28 degrees can also be expressed using the equivalent of the given angle (28 degrees) in radians (0.48869 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 28 degrees = 28° × (π/180°) rad = 7π/45 or 0.4886 . . .
∴ sec 28° = sec(0.4886) = 1.1325700. . .
Explanation:
For sec 28 degrees, the angle 28° lies between 0° and 90° (First Quadrant). Since secant function is positive in the first quadrant, thus sec 28° value = 1.1325700. . .
Since the secant function is a periodic function, we can represent sec 28° as, sec 28 degrees = sec(28° + n × 360°), n ∈ Z.
⇒ sec 28° = sec 388° = sec 748°, and so on.
Note: Since, secant is an even function, the value of sec(28°) = sec(28°).
Methods to Find Value of Sec 28 Degrees
The secant function is positive in the 1st quadrant. The value of sec 28° is given as 1.13257. . .. We can find the value of sec 28 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Sec 28 Degrees Using Unit Circle
To find the value of sec 28 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 28° angle with the positive xaxis.
 The sec of 28 degrees equals the reciprocal of the xcoordinate(0.8829) of the point of intersection (0.8829, 0.4695) of unit circle and r.
Hence the value of sec 28° = 1/x = 1.1326 (approx)
Sec 28° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec 28 degrees as:
 ± 1/√(1  sin²(28°))
 ± √(1 + tan²(28°))
 ± √(1 + cot²(28°))/cot 28°
 ± cosec 28°/√(cosec²(28°)  1)
 1/cos 28°
Note: Since 28° lies in the 1st Quadrant, the final value of sec 28° will be positive.
We can use trigonometric identities to represent sec 28° as,
 sec(180°  28°) = sec 152°
 sec(180° + 28°) = sec 208°
 cosec(90° + 28°) = cosec 118°
 cosec(90°  28°) = cosec 62°
☛ Also Check:
Examples Using Sec 28 Degrees

Example 1: Find the value of 1/(cos² 14°  sin² 14°). [Hint: Use sec 28° = 1.1326]
Solution:
Using the cos 2a formula,
1/(cos² 14°  sin² 14°) = 1/cos(2 × 14°) = sec 28°
∵ sec 28° = 1.1326
⇒ 1/(cos² 14°  sin² 14°) = 1.1326 
Example 2: Using the value of sec 28°, solve: (1 + tan²(28°)).
Solution:
We know, (1 + tan²(28°)) = (sec²(28°)) = 1.2827
⇒ (1 + tan²(28°)) = 1.2827 
Example 3: Find the value of sec 28° if cos 28° is 0.8829.
Solution:
Since, sec 28° = 1/cos 28°
⇒ sec 28° = 1/0.8829 = 1.1326
FAQs on Sec 28 Degrees
What is Sec 28 Degrees?
Sec 28 degrees is the value of secant trigonometric function for an angle equal to 28 degrees. The value of sec 28° is 1.1326 (approx).
How to Find Sec 28° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec 28° can be given in terms of other trigonometric functions as:
 ± 1/√(1sin²(28°))
 ± √(1 + tan²(28°))
 ± √(1 + cot²(28°))/cot 28°
 ± cosec 28°/√(cosec²(28°)  1)
 1/cos 28°
☛ Also check: trigonometric table
What is the Value of Sec 28° in Terms of Cosec 28°?
Since the secant function can be represented using the cosecant function, we can write sec 28° as [cosec 28°/√(cosec²(28°)  1)]. The value of cosec 28° is equal to 2.1300.
What is the Value of Sec 28 Degrees in Terms of Sin 28°?
Using trigonometric identities, we can write sec 28° in terms of sin 28° as, sec(28°) = 1/√(1  sin²(28°)). Here, the value of sin 28° is equal to 0.4695.
How to Find the Value of Sec 28 Degrees?
The value of sec 28 degrees can be calculated by constructing an angle of 28° with the xaxis, and then finding the coordinates of the corresponding point (0.8829, 0.4695) on the unit circle. The value of sec 28° is equal to the reciprocal of the xcoordinate(0.8829). ∴ sec 28° = 1.1326.
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