I have always wondered why you have to use sine and cosine instead of a proportional relationship, such as $(90-\text{angle})/90$. I cannot seem to find an answer anywhere online. Using my linear relationship, when the angle is $0$, then $90/90$ is $1$ and the component is at its maximum value, and when the angle is $90$, the component is $0$, both of which are true for cosine. But how come in between those values, there is a relationship of cosine?
For example, if there is a vector of $5$ at an angle $35$ degrees to the horizontal, why does the horizontal component have to be $5\cos 35^{\circ}$, why can't it be $5 \cdot (90-35)/90$?
Also, this leads me on to another question. Using the same example, if the vector is $5$ at $35$ degrees, then how can the sum of the horizontal and vertical components be greater than the original $5$? $5\cos 35^{\circ} + 5\sin 35^{\circ} = 6.96$ which is greater than $5$? Magic? Energy crisis solved?