What is the value of csc theta?

As the value of sin (θ ) approaches zero, however, the value of csc (θ ) tends to infinity. The value of csc (θ ) when sin (θ ) equals zero is thus said to be undefined.

What does csc theta equal?

The reciprocal sine function is cosecant, csc(theta)=1/sin(theta).

What is csc theta?

Cosecant Function: csc(θ) = Hypotenuse / Opposite. Secant Function: sec(θ) = Hypotenuse / Adjacent.

What is value of csc?

1 Answer. You cannot get an exact value; Considering that csc(x)=1sin(x) and that sin(π)=0 you get: csc(π)=1sin(π)=10 which cannot be calculated.

What is csc degree?

The csc trig function is periodic with a 360 -degree period. This property means that the function's values repeat every 360 degrees. In mathematical language, we can write this fact as sec(x) = sec(x + 360°) . The cosecant formula is not defined everywhere.

How To Find The Exact Values of Trig Functions

What's the derivative of csc?

The double derivative of csc x is csc x (cot²x + csc²x). The double derivative is nothing but the second derivative of a function which can be obtained by differentiating the first derivative of csc x.

What is sin if csc?

csc and sin are reciprocals of each other. That is, csc x = 1 / sin x, which also means that sin x = 1 / csc x.

For which value of theta is csc undefined?

csc(θ) is undefined at θ=0, θ=π and θ=2π , however we can get information about the behaviour csc(θ) close to these values using a claculator.

Where does csc equal root 2?

Trigonometry Examples

The exact value of arccsc(√2) is π4 . The cosecant function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from π to find the solution in the second quadrant.

What is the equivalent of sec θ?

Allied to these are the three reciprocal ratios, cosecant, secant and cotangent: cosecθ=hypotenuseopposite,secθ=hypotenuseadjacent,cotθ=adjacentopposite. cosecθ=1sinθ,secθ=1cosθ,cotθ=1tanθ.

Where does csc equal negative 1?

The exact value of arccsc(−1) is −π2 . The cosecant function is negative in the third and fourth quadrants.

What is the angle of θ?

If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse, the cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite side to the adjacent side.

What is this called θ?

Theta (uppercase Θ, lowercase θ) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth. In the system of Greek numerals it has a value of 9.

What is a theta in math?

The Greek letter θ (theta) is used in math as a variable to represent a measured angle. For example, the symbol theta appears in the three main trigonometric functions: sine, cosine, and tangent as the input variable. cos(θ)

How do you get sin theta from csc theta?

The reciprocal sine function is cosecant, csc(theta)=1/sin(theta). The reciprocal tangent function is cotangent, expressed two ways: cot(theta)=1/tan(theta) or cot(theta)=cos(theta)/sin(theta).

Does csc equal sin 1?

It is important to note that there is a big difference between the reciprocal value csc θ and sin^-1x. The cosecant function means 1/sin θ, while the second involves finding an angle whose sine is x.

What is the formula for sin theta?

The sine of an angle of a right-angled triangle is the ratio of its perpendicular (that is opposite to the angle) to the hypotenuse. The sin formula is given as: sin θ = Perpendicular / Hypotenuse. sin(θ + 2nπ) = sin θ for every θ

How do you find the exact value of csc pi 4?

The value of csc pi/4 can be calculated by constructing an angle of π/4 radians with the x-axis, and then finding the coordinates of the corresponding point (0.7071, 0.7071) on the unit circle. The value of cosec pi/4 is equal to the reciprocal of the y-coordinate (0.7071). ∴ csc pi/4 = 1.4142.