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The answer will depends on how the function is defined.
The sine function is usually introduced in mathematics as a trigonometric ratio: the ratio of the opposite side and the hypotenuse in a right angled triangle. Thanks to Pythagoras, the hypotenuse must be the largest side in a triangle and that means that the absolute value of the sine function must be less than 1.
Alternatively, if you can establish the identity
sin2(A) + cos2(A) = 1 then it follows that these bounds apply.
An equivalent definition, in terms of coordinate geometry is sine(A) = y/sqrt(x2+y2) where the line joining P(x,y) to the origin makes an angle of A with the x axis. It is easy to show that sin(A) must therefore lie between -1 and 1. The negative values of the sine function occur when the angle in question is in the third or fourth quadrants so that y is negative.
The more advanced definition for the sine function is
sin(a) = a/1! - a3/3! + a5/5! - a7/7! + ... where the angle a is measured in radians. It can be shown that this function is equivalent to the trigonometric definition.
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Is sin b equals 2.4 possible?
No. The absolute value of the sin function cannot exceed 1.
What is angle a when given sin a 312?
The absolute value of the sine function cannot exceed 1 and so sin(a) = 312 is not possible.
What is the arc function for trigonometric relationships?
The trigonometric function of an angle gives a certain value The arc trigonometric function of value is simply the angle For example, if sin (30 degrees) = 0.500 then arc sine ( 0.500) = 30 degrees
Why is 2 the answer for amplitude of y equals -2 sin x?
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How do you determine that the amplitude of y equals -2 sin x?
The amplitude of a function is half the distance between the maximum and minimum values. This is the absolute value of the number in front of the trig function. for example, y=Asin(x) or y= Acos(x) the absolute value of A is the amplitude. Therefore, the amplitude of y=-2sinx is 2
The function y equals sin θ is not a function beacause sin 30 equals sin 150?
Y=sin X is a function because for each value of X, there is exactly one Y value.
Is sin b equals 2.4 possible?
No. The absolute value of the sin function cannot exceed 1.
What is the maximum value that the graph of ycosx assume?
Both the function "cos x" and the function "sin x" have a maximum value of 1, and a minimum value of -1.
What is the maximum value of 3sinx plus 2?
The sine function (sin x) can only have values in the range between 1 and -1. Perhaps you can work it out from there.
What is angle a when given sin a 312?
The absolute value of the sine function cannot exceed 1 and so sin(a) = 312 is not possible.
What is the significance of the x-value in a sine wave function?
The answer will depend on where, in the sine function, the x-value appears: For example, its roles in f(x) = sin(x), or f(x, theta) = x*sin(theta) or f(x, theta) = sin(x*theta) f(theta) = sin(theta + x) are quite different.
Why the value of tan A is always less than one?
The values of tan are limitless (that is to say, within [-inf, inf]). However, sin and cos ratios are between -1 and 1. Think about it: sin = opposite/hypotenuse. Since hypotenuse is always larger than or equal to opposite, sin must always be less than 1. Same with cos.
2 sin x - 3 equals 0?
2 sin(x) - 3 = 0 2 sin(x) = 3 sin(x) = 1.5 No solution. The maximum value of the sine function is 1.0 .
What is sine reciprocal?
The reciprocal of sine is sin(-1). -1 being above the sin in small text like a squared number. * * * * * NO! sin-1 is the inverse function of sin, and that is not the same as the reciprocal. The reciprocal of sin(x) is 1/(sin(x) which is cosec(x). The following simple example will illustrate the difference between a reciprocal and inverse. Consider the function which doubles the value of its argument. That is f(x) = 2x The inverse of f(x) is the function g which halves its argument ie g(x) = x/2. The function g(x) reverses the action of f(x) and f(x) reverses g(x). Thus f[g(x)] = x for all x. The reciprocal of f(x) is 1/f(x) = 1/2x. So that for any value x, f(x) multiplied by its reciprocal (if it exists) always equals 1.
Is it a function if the range is repeated?
Yes. As long as there is only 1 value for each argument, it is a function. For example, the range of the sine function (y = sin x), for real values of x, consists of all the real numbers from -1 to 1 inclusive, and this range repeats infinitely many times. But for each value of x, there is only 1 value of sin x.
Approximation of sin x by x?
the value of sin(x) lies between -1 to +1. the approx value of sin(x)/x = 1 when x tends to 0 & sin(x)/x = 0 when x tends to infinity.
What is the arc function for trigonometric relationships?
The trigonometric function of an angle gives a certain value The arc trigonometric function of value is simply the angle For example, if sin (30 degrees) = 0.500 then arc sine ( 0.500) = 30 degrees
