Sec 450 Degrees

The value of Sec 450 degrees is undefined(∞). Sec 450 degrees in radians is written as sec (450° × π/180°), i.e., sec (5π/2) or sec (7.853981. . .). In this article, we will discuss the methods to find the value of sec 450 degrees with examples.

• Sec 450°: undefined(∞)
• Sec (-450 degrees): undefined(∞)
• Sec 450° in radians: sec (5π/2) or sec (7.8539816 . . .)

What is the Value of Sec 450 Degrees?

The value of sec 450 degrees is undefined(∞). Sec 450 degrees can also be expressed using the equivalent of the given angle (450 degrees) in radians (7.85398 . . .)

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 450 degrees = 450° × (π/180°) rad = 5π/2 or 7.8539 . . .
∴ sec 450° = sec(7.8539) = undefined(∞)

Explanation:

For sec 450°, the angle 450° > 360°. Given the periodic property of the secant function, we can represent it as sec(450° mod 360°) = sec(90°). The angle 450°, coterminal to angle 90°, lies on the positive y-axis.
Thus sec 450 degrees value = undefined(∞)
Similarly, sec 450° can also be written as, sec 450 degrees = (450° + n × 360°), n ∈ Z.
⇒ sec 450° = sec 810° = sec 1170°, and so on.
Note: Since, secant is an even function, the value of sec(-450°) = sec(450°) = undefined.

Methods to Find Value of Sec 450 Degrees

The value of sec 450° is given as undefined(∞). We can find the value of sec 450 degrees by:

• Using Trigonometric Functions
• Using Unit Circle

Sec 450° in Terms of Trigonometric Functions

Using trigonometry formulas, we can represent the sec 450 degrees as:

• ± 1/√(1 - sin²(450°))
• ± √(1 + tan²(450°))
• ± √(1 + cot²(450°))/cot 450°
• ± cosec 450°/√(cosec²(450°) - 1)
• 1/cos 450°

Note: Since 450° lies on the positive y-axis, the final value of sec 450° is undefined.

We can use trigonometric identities to represent sec 450° as,

• -sec(180° - 450°) = -sec(-270°)
• -sec(180° + 450°) = -sec 630°
• cosec(90° + 450°) = cosec 540°
• cosec(90° - 450°) = cosec(-360°)

Sec 450 Degrees Using Unit Circle

To find the value of sec 450 degrees using the unit circle, represent 450° in the form (1 × 360°) + 90° [∵ 450°>360°] ∵ secant is a periodic function, sec 450° = sec 90°.

• Rotate ‘r’ anticlockwise to form 90° or 450° angle with the positive x-axis.
• The sec of 450 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 450° = 1/x = undefined(∞) 

☛ Also Check:

• sec 75 degrees
• sec 30 degrees
• sec 225 degrees
• sec 135 degrees
• sec 405 degrees
• sec 510 degrees

FAQs on Sec 450 Degrees

What is Sec 450 Degrees?

Sec 450 degrees is the value of secant trigonometric function for an angle equal to 450 degrees. The value of sec 450° is undefined(∞).

What is the Exact Value of Sec 450 Degrees?

The exact value of sec 450 degrees is given as undefined(∞).

How to Find the Value of Sec 450 Degrees?

The value of sec 450 degrees can be calculated by constructing an angle of 450° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sec 450° is equal to the reciprocal of the x-coordinate(0). ∴ sec 450° = undefined(∞)

How to Find Sec 450° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of sec 450° can be given in terms of other trigonometric functions as:

• ± 1/√(1-sin²(450°))
• ± √(1 + tan²(450°))
• ± √(1 + cot²(450°))/cot 450°
• ± cosec 450°/√(cosec²(450°) - 1)
• 1/cos 450°

☛ Also check: trigonometric table

What is the Value of Sec 450 Degrees in Terms of Cot 450°?

We can represent the secant function in terms of the cotangent function using trig identities, sec 450° can be written as √(1 + cot²(450°))/cot 450°. Here, the value of cot 450° is equal to 0.