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Sec 7pi/4
The value of sec 7pi/4 is 1.4142135. . .. Sec 7pi/4 radians in degrees is written as sec ((7π/4) × 180°/π), i.e., sec (315°). In this article, we will discuss the methods to find the value of sec 7pi/4 with examples.
 Sec 7pi/4: √2
 Sec 7pi/4 in decimal: 1.4142135. . .
 Sec (7pi/4): 1.4142135. . . or √2
 Sec 7pi/4 in degrees: sec (315°)
What is the Value of Sec 7pi/4?
The value of sec 7pi/4 in decimal is 1.414213562. . .. Sec 7pi/4 can also be expressed using the equivalent of the given angle (7pi/4) in degrees (315°).
We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ 7pi/4 radians = 7pi/4 × (180°/pi) = 315° or 315 degrees
∴ sec 7pi/4 = sec 7π/4 = sec(315°) = √2 or 1.4142135. . .
Explanation:
For sec 7pi/4, the angle 7pi/4 lies between 3pi/2 and 2pi (Fourth Quadrant). Since secant function is positive in the fourth quadrant, thus sec 7pi/4 value = √2 or 1.4142135. . .
Since the secant function is a periodic function, we can represent sec 7pi/4 as, sec 7pi/4 = sec(7pi/4 + n × 2pi), n ∈ Z.
⇒ sec 7pi/4 = sec 15pi/4 = sec 23pi/4 , and so on.
Note: Since, secant is an even function, the value of sec(7pi/4) = sec(7pi/4).
Methods to Find Value of Sec 7pi/4
The secant function is positive in the 4th quadrant. The value of sec 7pi/4 is given as 1.41421. . .. We can find the value of sec 7pi/4 by:
 Using Unit Circle
 Using Trigonometric Functions
Sec 7pi/4 Using Unit Circle
To find the value of sec 7π/4 using the unit circle:
 Rotate ‘r’ anticlockwise to form 7pi/4 angle with the positive xaxis.
 The sec of 7pi/4 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 7pi/4 = 1/x = 1.4142 (approx)
Sec 7pi/4 in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec 7pi/4 as:
 ± 1/√(1  sin²(7pi/4))
 ± √(1 + tan²(7pi/4))
 ± √(1 + cot²(7pi/4))/cot(7pi/4)
 ± cosec(7pi/4)/√(cosec²(7pi/4)  1)
 1/cos(7pi/4)
Note: Since 7pi/4 lies in the 4th Quadrant, the final value of sec 7pi/4 will be positive.
We can use trigonometric identities to represent sec 7pi/4 as,
 sec(pi  7pi/4) = sec(3pi/4)
 sec(pi + 7pi/4) = sec 11pi/4
 cosec(pi/2 + 7pi/4) = cosec 9pi/4
 cosec(pi/2  7pi/4) = cosec(5pi/4)
☛ Also Check:
Examples Using Sec 7pi/4

Example 1: Find the value of sec 7pi/4 if cos 7pi/4 is 0.7071.
Solution:
Since, sec 7pi/4 = 1/cos(7pi/4)
⇒ sec 7pi/4 = 1/0.7071 = 1.4142 
Example 2: Using the value of sec 7pi/4, solve: (1 + tan²(7pi/4)).
Solution:
We know, (1 + tan²(7pi/4)) = (sec²(7pi/4)) = 2
⇒ (1 + tan²(7pi/4)) = 2 
Example 3: Find the value of 2 sec(7pi/4)/3 cosec(5pi/4).
Solution:
Using trigonometric identities, we know, sec(7pi/4) = cosec(pi/2  7pi/4) = cosec(5pi/4)
⇒ sec(7pi/4) = cosec(5pi/4)
⇒ Value of 2 sec(7pi/4)/3 cosec(5pi/4) = 2/3
FAQs on Sec 7pi/4
What is Sec 7pi/4?
Sec 7pi/4 is the value of secant trigonometric function for an angle equal to 7π/4. The value of sec 7pi/4 is √2 or 1.4142 (approx).
How to Find Sec 7pi/4 in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec 7pi/4 can be given in terms of other trigonometric functions as:
 ± 1/√(1  sin²(7pi/4))
 ± √(1 + tan²(7pi/4))
 ± √(1 + cot²(7pi/4))/cot(7pi/4)
 ± cosec(7pi/4)/√(cosec²(7pi/4)  1)
 1/cos(7pi/4)
☛ Also check: trigonometric table
What is the Value of Sec 7pi/4 in Terms of Cosec 7pi/4?
Since the secant function can be represented using the cosecant function, we can write sec 7pi/4 as [cosec(7pi/4)/√(cosec²(7pi/4)  1)]. The value of cosec 7pi/4 is equal to 1.4142.
What is the Value of Sec 7pi/4 in Terms of Sin 7pi/4?
Using trigonometric identities, we can write sec 7pi/4 in terms of sin 7pi/4 as, sec(7pi/4) = 1/√(1  sin²(7pi/4)). Here, the value of sin 7pi/4 is equal to 0.7071.
How to Find the Value of Sec 7pi/4?
The value of sec 7pi/4 can be calculated by constructing an angle of 7π/4 radians with the xaxis, and then finding the coordinates of the corresponding point (0.7071, 0.7071) on the unit circle. The value of sec 7pi/4 is equal to the reciprocal of the xcoordinate(0.7071). ∴ sec 7pi/4 = 1.4142.
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