Cosec 90

Cosec 90 Degrees

The value of
cosec 90 degrees is one. Cosec 90 degrees in radians is written as cosec (90° × π/180°), i.east., cosec (π/2) or cosec (1.570796. . .). In this article, we will hash out the methods to notice the value of cosec 90 degrees with examples.

• Cosec 90°:
  1
• Cosec (-90 degrees):
  -1
• Cosec 90° in radians:
  
  cosec (π/2) or cosec (1.5707963 . . .)

What is the Value of Cosec xc Degrees?

The value of cosec 90 degrees is ane. Cosec ninety degrees can too be expressed using the equivalent of the given bending (90 degrees) in radians (1.57079 . . .).

We know, using degree to radian conversion, θ in radians = θ in degrees × (pi/180°)
⇒ xc degrees = 90° × (π/180°) rad = π/2 or 1.5707 . . .
∴ cosec 90° = cosec(1.5707) = one

Explanation:

For cosec ninety degrees, the angle xc° lies on the positive y-axis. Thus cosec 90° value = ane
Since the cosecant function is a periodic function, we can represent cosec ninety° equally, cosec 90 degrees = cosec(90° + n × 360°), due north ∈ Z.
⇒ cosec xc° = cosec 450° = cosec 810°, so on.
Notation:
Since, cosecant is an odd function, the value of cosec(-90°) = -cosec(xc°).

Methods to Notice Value of Cosec 90 Degrees

The value of cosec xc° is given every bit one. We can find the value of cosec 90 degrees past:

• Using Unit Circle
• Using Trigonometric Functions

Cosec 90 Degrees Using Unit Circumvolve

To find the value of cosec 90 degrees using the unit of measurement circumvolve:

• Rotate ‘r’ anticlockwise to course 90° angle with the positive 10-axis.
• The cosec of ninety degrees equals the reciprocal of the y-coordinate(1) of the betoken of intersection (0, 1) of unit circle and r.

Hence the value of cosec xc° = 1/y = 1

Cosec 90° in Terms of Trigonometric Functions

Using trigonometry formulas, we can stand for the cosec 90 degrees equally:

• ± 1/√(ane-cos²(90°))
• ± √(1 + tan²(90°))/tan ninety°
• ± √(i + cot²(90°))
• ± sec 90°/√(sec²(xc°) – 1)
• 1/sin 90°

Nosotros can use trigonometric identities to stand for cosec 90° as,

• cosec(180° – xc°) = cosec 90°
• -cosec(180° + 90°) = -cosec 270°
• sec(xc° – xc°) = sec 0°
• -sec(90° + 90°) = -sec 180°

Note: Since 90° lies on the positive y-centrality, the final value of cosec 90° volition be positive.

☛ Besides Bank check:

• cosec 60 degrees
• cosec 20 degrees
• cosec 45 degrees
• cosec 1200 degrees
• cosec 0 degrees
• cosec 30 degrees

FAQs on Cosec 90 Degrees

What is Cosec xc Degrees?

Cosec 90 degrees is the value of cosecant trigonometric function for an bending equal to 90 degrees.


The value of cosec 90° is 1.

How to Notice the Value of Cosec 90 Degrees?

The value of cosec 90 degrees can exist calculated by constructing an angle of 90° with the x-axis, and and then finding the coordinates of the corresponding indicate (0, ane) on the unit circle. The value of cosec xc° is equal to the reciprocal of the y-coordinate (1). ∴ cosec 90° = ane.

How to Observe Cosec 90° in Terms of Other Trigonometric Functions?

Using trigonometry formula, the value of cosec 90° can be given in terms of other trigonometric functions as:

• ± 1/√(1-cos²(ninety°))
• ± √(1 + tan²(xc°))/tan 90°
• ± √(1 + cot²(ninety°))
• ± sec 90°/√(sec²(90°) – 1)
• 1/sin 90°

☛ Also check: trigonometry table

What is the Value of Cosec 90 Degrees in Terms of Cot 90°?

We can represent the cosec function in terms of the cotangent function using trig identities, cosec 90° can exist written as √(1 + cot²(90°)). Here, the value of cot 90° is equal to 0.

What is the Exact Value of Cosec xc Degrees?

The
exact value of cosec 90 degrees
is ane.