## anonymous one year ago 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).

1. anonymous

@Hero @ganeshie8

2. anonymous

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

3. anonymous

yes

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

well, as Deeezzzz pointed out, use your Unit Circle

9. anonymous

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