 In this video we provide the solution to question number three for the practice exam number two for math 1060 In which case we're trying to find an equation to match the graph of the provided trigonometric function right here So when we look at this the basic shape of this thing looks like it's a sinusoidal wave That is it's a sine or a cosine Looking at the graph because we start at the midline right here This makes me want to do a sine wave also as it's a multiple choice question Every option is in terms of sine so we should be doing this as a sine wave The most general sine wave would look like y equals some amplitude times sine Times you could have some coefficient. You could have some type of shift some type of x minus h over b like so plus Okay, this is the most general form we could see now when we look at this thing the amplitude can be found as The distance well, let's first mention the midline which is going to be right here It's just the x-axis since the midline is the x-axis it would appear that no type of vertical shift is going on whatsoever Also, since we're starting at the origin for a sine wave There's not any horizontal shift going on as well The next thing to notice is that the amplitude is going to be how far above or below the midline Does our sine wave go it goes all the way up to 2 so we see that a is good equal to right here And so the last thing to consider then would be the period How off how long does it take to repeat one cycle which we see on the screen right here? We start at zero we end at 2 pi right here. So the period B Well, excuse me that this coefficient B, which is related to the period It's going to be 2 pi over the period which we see the period here is is 2 pi the period Let's make that specific is 2 pi right here. So B is just going to turn out to be one So simplifying this thing we see that our function is just going to be y equals 2 sine of x And so we see the correct answer of each choice D