I need help with trigonometry. We are working on the features of graphs of cosine, sine, and tangent. We are comparing graph features, like minimum, maximum, period, and intrevals. We are also doing the unit circle. I'm really lost. I need explaination. Please help? I really appreciate it.
+227 Hmmm... Well, let's start with the unit circle. It'll be your BEST friend in later math classes (Trust me, I'm in AP Calc AB.) 
So, the unit circle is a circle whose center lies on the origin and whose radius is one. The unit circle has coordinates at every few degrees or radians, which we'll call θ. The coordinates are in this order: (Cosine θ, Sine θ). So, what this tells you is the cosine and sine of each angle given to you! For example, the coordinates at 30° or π/6 radians are: (√(3)/2 , 1/2). And so what? Well, using what we just learned a couple sentences ago, we now know that the cosine of 30° is √(3)/2, and the sine of 30° is 1/2! Easy, right? Just memorize the unit circle, and trig will be a LOT easier.
Sine... Well, let's look at the sine wave.
The sine wave tells you the value of the sine for different values of θ. Let's make f(x)=sine(x). Just a simple little function. Now, say we wanted to know the value of the sine at 150°, or 5π/6 radians. Well, just make x equal 5π/6, and plug it in! So, f(5π/6)=sine(5π/6)=1/2! (This is mainly with a calculator, though.)
Another thing about sine: When using it in triangle, remember that sine(θ)=Opposite Side / Hypotenuse. (SOH, if you want to remember it this way.) So, If you know two of these three things, you can figure out the last one! Neat, right?
Cosine... Let's look at the graph of cosine.
It looks like the sine wave, right? Well, they're different. Cosine's y-intercept is at y=1, whereas sine's y-intercept is at y=0. It's the same thing as before with sine: Make f(x)=cosine(x), blah blah blah.
When using cosine in a triangle, remember: cosine(θ)=Adjacent Side(The leg right next to the angle) / Hypotenuse. (This one is CAH.) Again, same rules as above.
Tangent... Yay. Let's see this fun graph:
Whoa, what happened there? That looks NOTHING like sine or cosine! Why???
Well, tangent(x)=sine(x)/cosine(x). So, of course the graph looks different! Remember, there are vertical asymptotes at every multiple of π/2. Again, plug in tangent(x) to f(x), blah blah.
In a triangle, tangent(θ)=Opposite Side / Adjacent Side. (This one: TOA.)
There ya go! Remember (cosine(x), sine(x)) for coordinates and SOH-CAH-TOA for triangles, and you should do just fine!
