Even though each trigonometry function is perfectly wonderful, being able to express each trig function in terms of one of the other five trig functions is frequently to your advantage. For example, you may have some sine terms in an expression that you want to express in terms of cosine, so that all the functions match, making it easier to solve an equation.
You can express the sine function in terms of cosine without doing much work. Starting with the Pythagorean identity involving sinθ and cosθ, subtract cos2θ from each side and take the square root of each side:
