Question

if arcsinA=5/8 , what does SinA =?

Answer 1

\(\bf sin^{-1}(A)=\cfrac{5}{8}\implies sin\left[sin^{-1}( {\color{brown}{ A }}) \right]=sin\left( \cfrac{5}{8}\right)
\\ \quad \\
recall\implies sin[sin^{-1}({\color{brown}{ 123}})]={\color{brown}{ 123}}\qquad sin^{-1}[sin^{}({\color{brown}{ \theta}})]={\color{brown}{ \theta}}\)

Answer 2

well...hmmm you don't really need to take sin() to both sides anyhow
though you needed the "A" value

but notice that line below anyhow

Answer 3

so the answer is 5/8?

Answer 4

well... close not quite
we first off, want to know ... something

keep in mind that a inverse trig function, "takes a value" and "returns an angle"
so

Answer 5

\(\bf sin^{-1}(A)=\cfrac{5}{8}\implies sin\left[sin^{-1}( {\color{brown}{ A }}) \right]=sin\left( \cfrac{5}{8}\right)
\\ \quad \\
recall\implies sin[sin^{-1}({\color{brown}{ 123}})]={\color{brown}{ 123}}\qquad sin^{-1}[sin^{}({\color{brown}{ \theta}})]={\color{brown}{ \theta}}
\\ \quad \\
sin\left[sin^{-1}( {\color{brown}{ A }}) \right]=sin\left( \cfrac{5}{8}\right)\implies A=sin\left( \cfrac{5}{8}\right)
\\ \quad \\

\textit{what's the }\ sin(A)?\qquad well
\\ \quad \\
sin(A)=sin\left[ sin\left( \cfrac{5}{8}\right) \right]\)

Answer 6

so the inverse function took the value returned an angle
sine of that angle is, well, whatever was inside the inverse function
that is value A

so to find what the sine of THAT value A is
we take out A, firstly
then take its sine

Answer 7

huh? its sina= sin(sin(5/8))???

Answer 8

yes, because, notice above
given value \(\Large \bf A\) is just a value

Answer 9

hehe....see it.? no?

the value A is inside the inverse function
we have to take it out to know what it's
once it's outside

we can just take the sine of it