Sec pi/4

The value of sec pi/4 is 1.4142135. . .. Sec pi/4 radians in degrees is written as sec ((π/4) × 180°/π), i.e., sec (45°). In this article, we will discuss the methods to find the value of sec pi/4 with examples.

• Sec pi/4: √2
• Sec pi/4 in decimal: 1.4142135. . .
• Sec (-pi/4): 1.4142135. . . or √2
• Sec pi/4 in degrees: sec (45°)

What is the Value of Sec pi/4?

The value of sec pi/4 in decimal is 1.414213562. . .. Sec pi/4 can also be expressed using the equivalent of the given angle (pi/4) in degrees (45°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)
⇒ pi/4 radians = pi/4 × (180°/pi) = 45° or 45 degrees
∴ sec pi/4 = sec π/4 = sec(45°) = √2 or 1.4142135. . .

Explanation:

For sec pi/4, the angle pi/4 lies between 0 and pi/2 (First Quadrant). Since secant function is positive in the first quadrant, thus sec pi/4 value = √2 or 1.4142135. . .
Since the secant function is a periodic function, we can represent sec pi/4 as, sec pi/4 = sec(pi/4 + n × 2pi), n ∈ Z.
⇒ sec pi/4 = sec 9pi/4 = sec 17pi/4 , and so on.
Note: Since, secant is an even function, the value of sec(-pi/4) = sec(pi/4).

Methods to Find Value of Sec pi/4

The secant function is positive in the 1st quadrant. The value of sec pi/4 is given as 1.41421. . .. We can find the value of sec pi/4 by:

• Using Trigonometric Functions
• Using Unit Circle

Sec pi/4 in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec pi/4 as:

• ± 1/√(1 - sin²(pi/4))
• ± √(1 + tan²(pi/4))
• ± √(1 + cot²(pi/4))/cot(pi/4)
• ± cosec(pi/4)/√(cosec²(pi/4) - 1)
• 1/cos(pi/4)

Note: Since pi/4 lies in the 1st Quadrant, the final value of sec pi/4 will be positive.

We can use trigonometric identities to represent sec pi/4 as,

• -sec(pi - pi/4) = -sec 3pi/4
• -sec(pi + pi/4) = -sec 5pi/4
• cosec(pi/2 + pi/4) = cosec 3pi/4
• cosec(pi/2 - pi/4) = cosec pi/4

Sec pi/4 Using Unit Circle

To find the value of sec π/4 using the unit circle:

• Rotate ‘r’ anticlockwise to form pi/4 angle with the positive x-axis.
• The sec of pi/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 pi/4 = 1/x = 1.4142 (approx)

☛ Also Check:

• tan 2pi
• sin 5pi/12
• cos 15pi/4
• sin 17pi/12
• cot 4pi/3
• sec 7pi/4

FAQs on Sec pi/4

What is Sec pi/4?

Sec pi/4 is the value of secant trigonometric function for an angle equal to π/4. The value of sec pi/4 is √2 or 1.4142 (approx).

What is the Value of Sec pi/4 in Terms of Tan pi/4?

We know, using trig identities, we can write sec pi/4 as √(1 + tan²(pi/4)). Here, the value of tan pi/4 is equal to 1.

How to Find Sec pi/4 in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec pi/4 can be given in terms of other trigonometric functions as:

• ± 1/√(1 - sin²(pi/4))
• ± √(1 + tan²(pi/4))
• ± √(1 + cot²(pi/4))/cot(pi/4)
• ± cosec(pi/4)/√(cosec²(pi/4) - 1)
• 1/cos(pi/4)

☛ Also check: trigonometric table

What is the Exact Value of Sec pi/4?

The exact value of sec pi/4 can be given accurately up to 8 decimal places as 1.41421356 or as √2.

How to Find the Value of Sec pi/4?

The value of sec pi/4 can be calculated by constructing an angle of π/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 pi/4 is equal to the reciprocal of the x-coordinate(0.7071). ∴ sec pi/4 = 1.4142.