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 x-axis.
• The sec of 7pi/4 equals the reciprocal of the x-coordinate(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:

• sin 7pi
• sin pi/3
• sin 5pi/12
• tan pi/8
• sin 7pi/4
• cos pi/8

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 x-axis, 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 x-coordinate(0.7071). ∴ sec 7pi/4 = 1.4142.