Question

Solve a given value of a sine graph

Answer 1

Given an equation:
\[y=20+12\sin\left(\frac{\pi \times x}{5}\right)\]Find the first x value where \(y=27\)

Answer 2

Since we are given the value of "y", let's replace it and try to solve for "x" to see if we can find a value for x that belongs to y=27:
\[27=20+12\sin (\frac{ \pi x }{ 5 })\]
Let's leave that sin alone on the right and sustract 20 from both sides, and divide 12 on both sides as well, after some aritmethic we get:
\[\frac{ (27-20) }{ 12 }= Sin(\frac{ \pi x }{ 5 })\]

Answer 3

Continuing on and operating:
\[\frac{ 7 }{ 12 } = Sin(\frac{ \pi x }{ 5 })\]
Now, let's take the inverse of Sin in both sides, so we can get rid of the Sin operation where the "X" is sitting, so we can more easily find it's value:
\[\sin^{-1} (\frac{ 7 }{ 12 })=\sin^{-1}( \sin (\frac{ \pi x }{ 5 }))\]
Since Sin^-1 is the inverse of Sin, we can cancel them, and end up with:
\[\frac{ \pi x }{ 5 }=\sin^{-1} (\frac{ 7 }{ 12 })\]
and ending with:
\[x=\frac{ 5\sin^{-1} (\frac{ 7 }{ 12 }) }{ \pi }\]
Now, That represents a number, all you have to do now is determine wich number it represents, and that will give you the value of "x".

Answer 4

not my problem but an excellent answer Owlcoffee
it helped me

Answer 5

No problem, that's why I'm here ;)