Question

Using the graph of y=sin(x), find the values of the interval [-4(pi), (pi)/2] that satisfy the ordered pair (x, 1/2).

Answer 1

@Hero @ganeshie8

Answer 2

\[is the interval (-4\pi,\pi/2)\]

Answer 3

yes

Answer 4

Do you have a unit circle ?
it is just asking for what values of x is sin 1/2
sin(x)=1/2

Answer 5

\(\bf y=sin(x)\qquad
\begin{array}{llll}
(x&\frac{1}{2})\\
\uparrow&\uparrow \\
x&y
\end{array}\implies \frac{1}{2}=sin(x)
\\ \quad \\
sin^{-1}\left( \cfrac{1}{2} \right)=sin^{-1}[sin(x)]\implies sin^{-1}\left( \cfrac{1}{2} \right)=x\)

Answer 6

so, find that angle, and any other angle with the same value in the range of \(\left[ -4\pi ,\frac{\pi }{2} \right]\)

Answer 7

so what are all the values that satisfy (x,1/2)

Answer 8

well, as Deeezzzz pointed out, use your Unit Circle

Answer 9

http://www.shelovesmath.com/wp-content/uploads/2012/11/Unit-Circle1.png <--- there's a unit circle

and check the coterminal angles on that given range