Sec 270 Degrees

The value of Sec 270 degrees is undefined. Sec 270 degrees in radians is written as sec (270° × π/180°), i.e., sec (3π/2) or sec (4.712388. . .). In this article, we will discuss the methods to find the value of sec 270 degrees with examples.

• Sec 270°: undefined
• Sec (-270 degrees): undefined
• Sec 270° in radians: sec (3π/2) or sec (4.7123889 . . .)

What is the Value of Sec 270 Degrees?

The value of sec 270 degrees is undefined. Sec 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123 . . .
∴ sec 270° = sec(4.7123) = undefined

Explanation:

For sec 270 degrees, the angle 270° lies on the negative y-axis. Thus, sec 270° value = undefined
Since the secant function is a periodic function, we can represent sec 270° as, sec 270 degrees = sec(270° + n × 360°), n ∈ Z.
⇒ sec 270° = sec 630° = sec 990°, and so on.
Note: Since, secant is an even function, the value of sec(-270°) = sec(270°) = undefined.

Methods to Find Value of Sec 270 Degrees

The value of sec 270° is given as undefined. We can find the value of sec 270 degrees by:

• Using Unit Circle
• Using Trigonometric Functions

Sec 270 Degrees Using Unit Circle

To find the value of sec 270 degrees using the unit circle:

• Rotate ‘r’ anticlockwise to form 270° angle with the positive x-axis.
• The sec of 270 degrees equals the reciprocal of the x-coordinate(0) of the point of intersection (0, -1) of unit circle and r.

Hence the value of sec 270° = 1/x = undefined 

Sec 270° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 270 degrees as:

• ± 1/√(1 - sin²(270°))
• ± √(1 + tan²(270°))
• ± √(1 + cot²(270°))/cot 270°
• ± cosec 270°/√(cosec²(270°) - 1)
• 1/cos 270°

We can use trigonometric identities to represent sec 270° as,

• -sec(180° - 270°) = -sec(-90°)
• -sec(180° + 270°) = -sec 450°
• cosec(90° + 270°) = cosec 360°
• cosec(90° - 270°) = cosec(-180°)

Note: Since 270° lies on the negative y-axis, the final value of sec 270° is undefined.

☛ Also Check:

• sec 120 degrees
• sec 47 degrees
• sec 405 degrees
• sec 390 degrees
• sec 510 degrees
• sec 90 degrees

FAQs on Sec 270 Degrees

What is Sec 270 Degrees?

Sec 270 degrees is the value of secant trigonometric function for an angle equal to 270 degrees. The value of sec 270° is undefined.

What is the Value of Sec 270 Degrees in Terms of Tan 270°?

We know, using trig identities, we can write sec 270° as √(1 + tan²(270°)). Here, the value of tan 270° is equal to undefined.

How to Find the Value of Sec 270 Degrees?

The value of sec 270 degrees can be calculated by constructing an angle of 270° with the x-axis, and then finding the coordinates of the corresponding point (0, -1) on the unit circle. The value of sec 270° is equal to the reciprocal of the x-coordinate(0). ∴ sec 270° = undefined.

How to Find Sec 270° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 270° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(270°))
• ± √(1 + tan²(270°))
• ± √(1 + cot²(270°))/cot 270°
• ± cosec 270°/√(cosec²(270°) - 1)
• 1/cos 270°

☛ Also check: trigonometric table

What is the Value of Sec 270° in Terms of Cosec 270°?

Since the secant function can be represented using the cosecant function, we can write sec 270° as -[cosec 270°/√(cosec²(270°) - 1)]. The value of cosec 270° is equal to -1.