Question

Give the equation of the graph pictured below

Answer 1

I believe the equation should be y = -0.5sin(x-2π)-2

Answer 2

Now, if you notice the picture below

the amplitude of the graph we have above, is squished by half, what in sin(θ) would be an amplitude of 1 above the red midline and 1 below it, for the graph above became 1/2 above the midline and 1/2 below it, for an amplitude of 1/2

now, sin(θ) starts off from 0 and goes up then down, now, if you simply give it a negative leading coefficient, the graph will flip upside-down, or -1/2

if we look at the period of the graph above, is 2π, and the period of sin(θ) is also 2π, so, no change on the period

but the graph above is shifted, from a midline at y = 0, to y = -2, so it has a vertical shift of -2

thus $\bf y=-\cfrac{1}{2}sin(\theta)-2$