9514 1404 393
Answer:
E. sin⁻¹(2.81/3.64)
Step-by-step explanation:
If you understand the question, you know that the relation of interest is ...
Sin = Opposite/Hypotenuse
sin(•) = 2.81/3.64
• = arcsin(2.81/3.64) . . . . matches choice E
If you want to find the angle, you need to use a function that gives the angle for a particular sine value. That function is called the arcsine function, or the inverse sine function. It is represented using the notation arcsin( ) or sin⁻¹( ). (The -1 is interpreted as being an exponent.)
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You may recall the rules of exponents say ...
s^-2 = 1/s^2
Then the simple reciprocal, or inverse, is ...
s^-1 = 1/s^1 = 1/s
That is, an exponent of -1 signifies an inverse. This is the notation of choice to signify an inverse function. It is applied to the function name. (It does not mean the reciprocal of the function value.)
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Additional comment
One needs to be careful with exponents on function names. An exponent of -1 on the name is generally understood to signify the inverse function.
Positive exponents greater than 1 can be ambiguous. Usually, we intend ...
[tex]\sin^2(x) = (\sin(x))^2[/tex]
Sometimes, we mean ...
[tex]f(f(x)) = f^2(x) \ne (f(x))^2 = f(x)^2[/tex]
