Dear members of the Math Help Forum,

I am going to be soon entering high school(the Finnish school system), and thus will be taking my first Calculus course. During the summer I decided to look at some pre-calculus topics, which are going to be quickly covered before moving on to calculus. Well, guess what? Two months hve gone by and I am still stuck on trigonometry.

When we studied trigonometry in comprehensive school(the right-angled triangles), I understood it fine, but as soon as my Calculus book started talking about the Unit circle and the cosine, sine and tangent functions, I just couldn't understand it anymore. So to this day I still am stuck on trigonometry.

For example, the exercise in my book asks me to prove cos^4x-sin^4x=cos(2x)

I was able to prove one of the addition formulas cos(s-t)=cos s cos t + sin s sin t, because the book provided a visual representation of what this formula is actually saying. However, for the formula above I just cannot draw any kind of representation.

I have tried to search for numerous solutions to my problem, but every book I read on the topic just seems to complicate it more.

If someone could please, explain to me the concept of Unit circle, and the basic idea of the trigonometric functions, and what they are used for in Calculus or refer me to a website, which explains the concept simply, I woul be very grateful.

Thank you in advance!