Sec 90 Degrees
The value of Sec 90 degrees is undefined(or, ∞). Sec 90 degrees in radians is written as sec (90° × π/180°), i.e., sec (π/2) or sec (1.570796. . .). In this article, we will discuss the methods to find the value of sec 90 degrees with examples.
 Sec 90°: undefined(∞)
 Sec (90 degrees): undefined
 Sec 90° in radians: sec (π/2) or sec (1.5707963 . . .)
What is the Value of Sec 90 Degrees?
The value of sec 90 degrees is undefined(∞). Sec 90 degrees can also be expressed using the equivalent of the given angle (90 degrees) in radians (1.57079 . . .)
We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ 90 degrees = 90° × (π/180°) rad = π/2 or 1.5707 . . .
∴ sec 90° = sec(1.5707) = undefined(∞)
Explanation:
For sec 90 degrees, the angle 90° lies on the positive yaxis. Thus, sec 90° value = undefined(∞)
Since the secant function is a periodic function, we can represent sec 90° as, sec 90 degrees = sec(90° + n × 360°), n ∈ Z.
⇒ sec 90° = sec 450° = sec 810°, and so on.
Note: Since, secant is an even function, the value of sec(90°) = sec(90°) = undefined.
Methods to Find Value of Sec 90 Degrees
The value of sec 90° is given as undefined(∞). We can find the value of sec 90 degrees by:
 Using Unit Circle
 Using Trigonometric Functions
Sec 90 Degrees Using Unit Circle
To find the value of sec 90 degrees using the unit circle:
 Rotate ‘r’ anticlockwise to form 90° angle with the positive xaxis.
 The sec of 90 degrees equals the reciprocal of the xcoordinate(0) of the point of intersection (0, 1) of unit circle and r.
Hence the value of sec 90° = 1/x = undefined(∞)
Sec 90° in Terms of Trigonometric Functions
Using trigonometry formulas, we can represent the sec 90 degrees as:
 ± 1/√(1  sin²(90°))
 ± √(1 + tan²(90°))
 ± √(1 + cot²(90°))/cot 90°
 ± cosec 90°/√(cosec²(90°)  1)
 1/cos 90°
We can use trigonometric identities to represent sec 90° as,
 sec(180°  90°) = sec 90°
 sec(180° + 90°) = sec 270°
 cosec(90° + 90°) = cosec 180°
 cosec(90°  90°) = cosec 0°
Note: Since 90° lies on the positive yaxis, the final value of sec 90° is undefined(∞).
☛ Also Check:
Examples Using Sec 90 Degrees

Example 1: Find the value of 2 sec(90°)/3 cosec(90°).
Solution:
Using trigonometric identities, we know, sec(90°) = undefined(∞) and cosec 90° = 1.
⇒ Value of 2 sec(90°)/3 cosec(90°) = undefined 
Example 2: Find the value of 1/(cos² 45°  sin² 45°). [Hint: Use sec 90° = undefined(∞)]
Solution:
Using the cos 2a formula,
1/(cos² 45°  sin² 45°) = 1/cos(2 × 45°) = sec 90°
∵ sec 90° = undefined(∞)
⇒ 1/(cos² 45°  sin² 45°) = undefined(∞) 
Example 3: Using the value of sec 90°, solve: (1 + tan²(90°)).
Solution:
We know, (1 + tan²(90°)) = (sec²(90°)) = undefined
FAQs on Sec 90 Degrees
What is Sec 90 Degrees?
Sec 90 degrees is the value of secant trigonometric function for an angle equal to 90 degrees. The value of sec 90° is undefined(∞).
What is the Value of Sec 90° in Terms of Cos 90°?
Since the cosine function is the reciprocal of the secant function, we can write sec 90° as 1/cos(90°). The value of cos 90° is equal to 0.
How to Find Sec 90° in Terms of Other Trigonometric Functions?
Using trigonometry formula, the value of sec 90° can be given in terms of other trigonometric functions as:
 ± 1/√(1sin²(90°))
 ± √(1 + tan²(90°))
 ± √(1 + cot²(90°))/cot 90°
 ± cosec 90°/√(cosec²(90°)  1)
 1/cos 90°
☛ Also check: trigonometry table
What is the Value of Sec 90 Degrees in Terms of Cot 90°?
We can represent the secant function in terms of the cotangent function using trig identities, sec 90° can be written as √(1 + cot²(90°))/cot 90°. Here, the value of cot 90° is equal to 0.
How to Find the Value of Sec 90 Degrees?
The value of sec 90 degrees can be calculated by constructing an angle of 90° with the xaxis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sec 90° is equal to the reciprocal of the xcoordinate(0). ∴ sec 90° = undefined(∞).
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