What is the difference between Cosec and arcsin?

The arcsin is the value of the angle whose sin is that number. The cosecant is 1 divided by the sin of the angle. Arcsin is the inverse trigonometric function of sine while cosecant is the reciprocal of sine. Since sine is opposite over hypotenuse, cosecant can be expressed as hypotenuse over opposite or 1/sine.

What’s the difference between inverse sin and arcsin?

What is the difference between sin-1 and 1/sin x? Sin-1 is the inverse of sine function. Arcsin α means the arc whose sine is α. Whereas 1/sin x shows the reciprocal of sine function, which is also equal to cosecant function.

Is cosecant the same as inverse sine?

Inverse Reciprocal Trigonometric Functions We already know that the cosecant function is the reciprocal of the sine function. This will be used to derive the reciprocal of the inverse sine function. Because cosecant and secant are inverses, \begin{align*}\sin^{-1} \frac{1}{x} = \csc^{-1} x\end{align*} is also true.

Is arcsin X the same as 1 sin x?

1 Expert Answer sin-1x means the same as arcsin x, i.e., the arc whose sine is x.

Is sin 1 the same as sin 1?

The notation sin-1(x) has been misunderstood to mean 1/sin(x). So sin-1(x) means the inverse sine of x, that is, the function that undoes the sine function. It is not equal to 1/sin(x).

How do you convert arcsin to sin?

The inverse sine function, arcsine, will take the ratio of the opposite/hypotenuse (x) and return the angle, θ. So, knowing that, for our triangle, arcsin(x) = θ we can also write that: Sine: sin(arcsin(x)) = x. Cosine: cos(arcsin(x)) = √(1-x²)

What is cosec in math?

Cosecant is one of the six trigonometric ratios which is also denoted as cosec or csc. The cosecant formula is given by the length of the hypotenuse divided by the length of the opposite side in a right triangle.

How are sine and cosecant related?

The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.

What is the difference between sin − 1 x and 1 sin x?

So sin^-1 x represents an angle whose sine is x. The second one sin (x) ^-1 is nothing but the reciprocal of sin x. Hence sin (x) ^-1 = 1/sin x denotes a value. Thus the first one represents an angle where as the second one denotes a value.

Is cosecant the inverse of arcsin?

Cosecant is a separate trigonometric function and not an inverse function like arcsin. Therefore, cosecant would not cancel a sine function out like arcsin would. Reciprocal and inverse are two vocabulary terms that mean different things. The arcsin is the value of the angle whose sin is that number.

What is the difference between csc(x)*sin(x) and arcsin(x)?

cosecant is the reciprical of the sin function or 1/sin(x) so that csc(x)*sin(x) = 1 when it is defined. The two can be confused since arcsin(x) is often denoted as sin^-1(x) and x^-1 is 1/x.

What is SEC secant cosec and cosec?

Sec, Cosec and Cot. Secant, cosecant and cotangent, almost always written as sec, cosec and cot are trigonometric functions like sin, cos and tan. Note, sec x is not the same as cos -1 x (sometimes written as arccos x).

What is the inverse sine function of sin(x)?

This raises some confusion when one denotes the inverse sine function as sin⁻¹ (x), because sin⁻¹ (x) does not equal (sin (x))⁻¹. In fact, (sin (x))⁻¹=csc (x). To avoid this confusion, the inverse sine function is usually denoted arcsin (x). arcsin (x) is the inverse to the function sin (x).