Sin-1 is the inverse of sine function. -1 here do not represent the exponent. 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.
1sinx=cscx by definition.
sin-1x means the same as arcsin x, i.e., the arc whose sine is x.
Graphs of Inverse Trigonometric FunctionsFunctionDomainRangesin−1(x)[−1,1][−π2,π2]cos−1(x)[−1,1][0,π]tan−1(x)(−∞,∞)(−π2,π2)cot−1(x)(−∞,∞)(0,π)
Answer: The expression 1 / sin x can be simplified as cosec x.
Answer: 1/sinx = cosec x. 1/cosx= sec x. 1/tanx = cot x.
π/2Value of the Inverse of Sin 1 (Sin -1 1) Since the inverse of sin-1 (1) is 90° or π/2, the maximum value of the sine function is denoted by '1'.
Note that the domain of the function y=sin(x) ) is all real numbers (sine is defined for any angle measure), the range is −1≤y≤1 .
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.
We denote the inverse function as y=sin−1(x) . It is read y is the inverse of sine x and means y is the real number angle whose sine value is x . Be careful of the notation used.
1-sinx = cos^2x/2+sin^2x/2 -2sinx/2.
Solutions for Trigonometric EquationsEquationsSolutionssin x = sin θx = nπ + (-1)nθ, where θ ∈ [-π/2, π/2]cos x = cos θx = 2nπ ± θ, where θ ∈ (0, π]tan x = tan θx = nπ + θ, where θ ∈ (-π/2 , π/2]sin 2x = sin 2θx = nπ ± θ•Sep 5, 2019
Answer: The expression 1 / sin x can be simplified as cosec x.
sin-1x means the same as arcsin x, i.e., the arc whose sine is x.
The exact value of sin-1(−1) is −π2 .
[−1,1]The domain of sin−1 is [−1,1] and its range is [−π2,π2]. We can see from the graph that sin−1 is an odd function, that is, sin−1(−x)=−sin−1x. We can also see that it is an increasing function.
The graph of y=sin(x) is like a wave that forever oscillates between -1 and 1, in a shape that repeats itself every 2π units. Specifically, this means that the domain of sin(x) is all real numbers, and the range is [-1,1].
The derivative of the sine inverse function is written as (sin-1x)' = 1/√(1-x2), that is, the derivative of sin inverse x is 1/√(1-x2). In other words, the rate of change of sin-1x at a particular angle is given by 1/√(1-x2), where -1 < x < 1.
all real numbersThe function f(x) = sin x has all real numbers in its domain, but its range is −1 ≤ sin x ≤ 1. The values of the sine function are different, depending on whether the angle is in degrees or radians. The function is periodic with periodicity 360 degrees or 2π radians.
Note that the arcsine function or sin−1x as it is common to write is the inverse function under composition not under multiplication. sin−1(x) doesn't mean 1sin(x). It means the inverse function of the sin (when restricted to a conventional interval).
Nope, those are the same. As long as you have the parentheses around the sin2x, the whole thing is squared. In a calculator, that is how you would put it if you wanted to take the sine of the angle 2x, then square the result.
The most commonly used formula of sin2x is twice the product of sine function and cosine function which is mathematically given by, sin2x = 2 sinx cosx.
How long does cooked tuna last at room temperature? Bacteria grow rapidly at temperatures between 40 °F and 140 °F, cooked tuna should be discarded if left for more than 2 hours at room temperature.
Tuna, however, should not be left unrefrigerated for more than two hours. Therefore, the maximum unrefrigerated exposure should be no more than two hours. If the space is warm, such as sunlight, greater than 90 degrees, and other conditions, two hours are reduced to one hour.
This proves that Wolverine is not able to live forever, even if his skeleton is composed of a virtually indestructible alloy. In "X-Men: Evolution" Wolverine was captured and fell from a plane and broke his arm. Despite being virtually indestructible, it took him a while before he fully recovered.