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Sec 225 Degrees
The value of Sec 225 degrees is 1.4142135. . .. Sec 225 degrees in radians is written as sec (225° × π/180°), i.e., sec (5π/4) or sec (3.926990. . .). In this article, we will discuss the methods to find the value of sec 225 degrees with examples.
 Sec 225°: √2
 Sec 225° in decimal: 1.4142135. . .
 Sec (225 degrees): 1.4142135. . . or √2
 Sec 225° in radians: sec (5π/4) or sec (3.9269908 . . .)
What is the Value of Sec 225 Degrees?
The value of sec 225 degrees in decimal is 1.414213562. . .. Sec 225 degrees can also be expressed using the equivalent of the given angle (225 degrees) in radians (3.92699 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 225 degrees = 225° × (π/180°) rad = 5π/4 or 3.9269 . . .
∴ sec 225° = sec(3.9269) = √2 or 1.4142135. . .
Explanation:
For sec 225 degrees, the angle 225° lies between 180° and 270° (Third Quadrant). Since secant function is negative in the third quadrant, thus sec 225° value = √2 or 1.4142135. . .
Since the secant function is a periodic function, we can represent sec 225° as, sec 225 degrees = sec(225° + n × 360°), n ∈ Z.
⇒ sec 225° = sec 585° = sec 945°, and so on.
Note: Since, secant is an even function, the value of sec(225°) = sec(225°).
Methods to Find Value of Sec 225 Degrees
The secant function is negative in the 3rd quadrant. The value of sec 225° is given as 1.41421. . .. We can find the value of sec 225 degrees by:
 Using Trigonometric Functions
 Using Unit Circle
Sec 225° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec 225 degrees as:
 ± 1/√(1  sin²(225°))
 ± √(1 + tan²(225°))
 ± √(1 + cot²(225°))/cot 225°
 ± cosec 225°/√(cosec²(225°)  1)
 1/cos 225°
Note: Since 225° lies in the 3rd Quadrant, the final value of sec 225° will be negative.
We can use trigonometric identities to represent sec 225° as,
 sec(180°  225°) = sec(45°)
 sec(180° + 225°) = sec 405°
 cosec(90° + 225°) = cosec 315°
 cosec(90°  225°) = cosec(135°)
Sec 225 Degrees Using Unit Circle
To find the value of sec 225 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 225° angle with the positive xaxis.
 The sec of 225 degrees equals the reciprocal of the xcoordinate(0.7071) of the point of intersection (0.7071, 0.7071) of unit circle and r.
Hence the value of sec 225° = 1/x = 1.4142 (approx)
☛ Also Check:
Examples Using Sec 225 Degrees

Example 1: Simplify: 7 (sec 225°/cosec 315°)
Solution:
We know sec 225° = cosec 315°
⇒ 7 sec 225°/cosec 315° = 7 (sec 225°/sec 225°)
= 7(1) = 7 
Example 2: Find the value of 1/(cos² 112.5°  sin² 112.5°). [Hint: Use sec 225° = 1.4142]
Solution:
Using the cos 2a formula,
1/(cos² 112.5°  sin² 112.5°) = 1/cos(2 × 112.5°) = sec 225°
∵ sec 225° = 1.4142
⇒ 1/(cos² 112.5°  sin² 112.5°) = 1.4142 
Example 3: Using the value of sec 225°, solve: (1 + tan²(225°)).
Solution:
We know, (1 + tan²(225°)) = (sec²(225°)) = 2
⇒ (1 + tan²(225°)) = 2
FAQs on Sec 225 Degrees
What is Sec 225 Degrees?
Sec 225 degrees is the value of secant trigonometric function for an angle equal to 225 degrees. The value of sec 225° is √2 or 1.4142 (approx).
How to Find the Value of Sec 225 Degrees?
The value of sec 225 degrees can be calculated by constructing an angle of 225° with the xaxis, and then finding the coordinates of the corresponding point (0.7071, 0.7071) on the unit circle. The value of sec 225° is equal to the reciprocal of the xcoordinate(0.7071). ∴ sec 225° = 1.4142.
How to Find Sec 225° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec 225° can be given in terms of other trigonometric functions as:
 ± 1/√(1sin²(225°))
 ± √(1 + tan²(225°))
 ± √(1 + cot²(225°))/cot 225°
 ± cosec 225°/√(cosec²(225°)  1)
 1/cos 225°
☛ Also check: trigonometry table
What is the Value of Sec 225° in Terms of Cosec 225°?
Since the secant function can be represented using the cosecant function, we can write sec 225° as [cosec 225°/√(cosec²(225°)  1)]. The value of cosec 225° is equal to 1.4142.
What is the Value of Sec 225 Degrees in Terms of Sin 225°?
Using trigonometric identities, we can write sec 225° in terms of sin 225° as, sec(225°) = 1/√(1  sin²(225°)). Here, the value of sin 225° is equal to 0.7071.
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