wolfishgirl wrote:why does math have to get harder as you get older? why why why!!!! why did i have to take Precalc!!! and how do you expect me to know how to graph y=cosx on the interval -90*</=x</=360*
* means degrees
</= means less than or equal to
I don't know how much you already know about trig, so I'll try to explain this in the most simple way I can.
Think about what cosine means. It's the ratio of the adjacent leg of a triangle to the triangle's hypotenuse, based on an angle. Like this, where the angle being measured is the Greek letter theta (θ).
So, let's assume theta is zero degrees, or a straight line. In this case, the adjacent leg and the hypotenuse are exactly the same. Since cosine is adjacent/hypotenuse, if the angle is zero, then cosine is going to equal one, because anything divided by itself is one.
Now, if you've taken geometry, then you'll know what the lengths of the legs will be if theta is 45 degrees. But if you don't remember that, it doesn't really matter. If the hypotenuse is 1, then both legs will be equal to the square root of two, divided by two. But that's not really important. All you need to know is that their length will be less than one, but still greater than zero. Just make some approximations, if you need to.
Now, you probably see where I'm going with this. Your equation is y=cos(x). You're graphing the values of what the adjacent length of a triangle is, based on what the angle is. But if you think about it for a minute, you'll notice that if you keep the same hypotenuse length, but only change theta, it starts to make a circle. Like this.
Now, think about this in terms of a circle, with zero degrees being at 3 o'clock, 90 degrees being at 12, 180 degrees being at 9, and 270 at 6. For negative degrees, you just go the other direction, so that -90 is equal to 270. Yes, it's an arbitrary system, but that's just the way we do it.
Hopefully, this should make sense now. To graph it, all you have to do is ask yourself what the horizontal distance is at a point on a circle with that angle, and a radius of 1. That distance becomes your height on a graph, and the angle is the x-axis.
So, now we can do this. At zero degrees, the horizontal distance is 1. As the angle increases from 0 to 90 degrees, the horizontal distance starts to decrease, until it hits zero at the top of the circle. Then the distance starts to go negative, until it hits 180 degrees, at which the horizontal distance is -1. Then it increases again, where it goes down to zero at 270 degrees. Then, just go back to one, and you've made it a full circle. So, if you graph it, it will look like this.
Your graph should look something like this.
But, since you have to graph it on the interval of -90 to 360 degrees, and because this is sin(x) instead of cos(x) yours will look slightly different. You just continue the wave pattern left a bit, so that at -90 degrees, you'll see the height at 0, and with 0 degrees, the height at 1. BAM! You're done.
Trig might seem intimidating, but don't worry about it. That's all you do in precalc, so you have the entire year to understand the material, and even then, you definitely aren't the only one who gets confused by this stuff. Most people will tell you they hate trig because it's too hard.
I hope that clears things up. As you can see, I'm a total math nerd. XD
...or you could just put it in your graphing calculator. That works too.
I'm thinking i should get something to eat and get my sister off of the bus.
