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I'm
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Homework Statement
arcsin(sin) = 1 right?
Homework Equations
The Attempt at a Solution
Basically, I see arcsin as 1/sin
is this correct?
Yes or no, depending on what you literally mean.I'm said:Oh I think I get it.
So, I can take the arcsine of both sides in a problem such as:
sin(2x) = (Root3 )/2
and I would get arcsin(sin(2x)) = arcsin ((root3)/2)
Which would get me to 2x = arcsin ((root3)/2)?
Correct?
Hurkyl said:Yes or no, depending on what you literally mean.
The big overwhelming obstacle that you need to make sure you understand is that the equation
sin(y)=xhas infinitely many solutions. (or zero solutions, if |x| > 1)
If I'm to define a function Arcsin(x) that gives a solution to sin(y)=x, I can only pick one of them. (The solution lying in [itex]-\pi/2 \leq y \leq \pi/2[/itex] is traditional)
So if I want all solutions to sin(y)=x, I have more work to do because Arcsin(x) gives me one of them. Fortunately, knowing one solution, it's easy to find all of the others. (If it's not obvious, study the graph of sin(y)=x for a while...)
In otherwords, Arcsin(sin(y)) is not y. It is "the number in [itex][-\pi/2 , \pi/2][/itex] that is related to y".
I'm said:Oh I think I get it.
So, I can take the arcsine of both sides in a problem such as:
sin(2x) = (Root3 )/2
and I would get arcsin(sin(2x)) = arcsin ((root3)/2)
Which would get me to 2x = arcsin ((root3)/2)?
Correct?
I'm said:so in this case would it be arcsin(sin(60)) = Arcsin (([tex]\sqrt{3}[/tex]/2
?
Can you give me a problem that displays what you have just told me? I'd really like to see one ( as I have not been told that in my Precalculus class).
Thanks.
Arcsin, or inverse sine, is a mathematical function that returns the angle whose sine is equal to a given value.
No, arcsin(sin) does not always equal 1. The value of arcsin(sin) depends on the input value for sine. However, if the input value for sine is 1, then arcsin(sin) will equal 1.
Yes, arcsin(sin) is typically used to find the angle associated with a given sine value. It is commonly used in trigonometry and geometry.
Yes, arcsin(sin) can have multiple solutions. This is because the sine function is periodic, meaning it repeats itself at regular intervals. As a result, there can be multiple angles that have the same sine value.
Arcsin(sin) is the inverse of the sine function, just as arccos(cos) is the inverse of the cosine function and arctan(tan) is the inverse of the tangent function. These inverse trigonometric functions are used to find the angle associated with a given trigonometric ratio.