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Csc Calculator

Write down the angle, and the free csc calculator will quickly find and calculate the cosecant or inverse cosecant values for it in degrees, radians, or Pi-radians.

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The online CSC Calculator helps you quickly find the value of the cosecant (csc) function for any angle in degrees, radians, or π radians. This guide also explains what csc is in trigonometry, along with formulas, tables, graphs, and key concepts.

What Is CSC in Math?

In trigonometry, the cosecant (csc) is the reciprocal of the sine function. For a right-angled triangle, it is defined as the ratio of the hypotenuse to the side opposite the given angle:

Cosecant Formula

$$ \csc(\theta) = \frac{\text{Hypotenuse}}{\text{Opposite}} \quad\text{or}\quad \csc(x) = \frac{1}{\sin(x)} $$

Use an online CSC Calculator for quick and accurate calculations.

How to Find CSC of an Angle?

To find the cosecant of an angle α:

Divide the hypotenuse by the opposite side of the triangle
Or simply take the reciprocal of sin(α)

For fast results, a CSC calculator can compute this instantly.

CSC Calculator Angle

You can also use the Secant Calculator for secant values.

Cosecant Table

Common csc values for standard angles:

Degrees	Radians	Cosecant (csc)
0°	0	Undefined
30°	π/6	2
45°	π/4	√2
60°	π/3	2√3 / 3
90°	π/2	1
120°	2π/3	2√3 / 3
135°	3π/4	√2
150°	5π/6	2
180°	π	Undefined

With a calculator, memorizing the table is unnecessary. You can also use the Arcsin Calculator to compute inverse sine values.

Cosecant Graph

The csc graph is made up of repeating U-shaped curves.

Cosecant Calculator Graph

Key properties of the cosecant graph:

CSC values are always |csc| ≥ 1
The graph never crosses the x-axis
Undefined at multiples of π (180°)

How the CSC Calculator Works

Input

Enter the angle value
Select degrees, radians, or π radians
Click the Calculate button

Output

Displays csc(θ) value
Allows multiple recalculations instantly

FAQs

How do you find CSC on the unit circle?

Use the y-coordinate of the corresponding point:

$$ \csc(t) = \frac{1}{y} $$

What are the six trigonometric functions?

Primary: sin, cos, tan

Reciprocal: csc, sec, cot

Basic Trigonometric Ratios

sin θ = Opposite / Hypotenuse
cos θ = Adjacent / Hypotenuse
tan θ = Opposite / Adjacent

Who is considered the father of trigonometry?

Hipparchus of Nicaea, known for developing trigonometric tables and angular measurements.

Conclusion

The CSC Calculator simplifies calculations in engineering, physics, navigation, and astronomy. It allows instant verification of cosecant values for any angle.

References

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