Like sine and cosine, the values of tangent (tan) of an angle Θ in a right triangle are also trigonometric ratios that relate the lengths of the sides of the triangle. Specifically, tan(Θ) is the ratio of the length of the side opposite the angle (opposite leg) to the length of the side adjacent to the angle (adjacent leg) in the right triangle.
While sine and cosine values can range from -1 to 1, the values of tangent can range from negative infinity to positive infinity, with vertical asymptotes at odd multiples of 90 degrees. This is because the tangent of an angle is undefined for values where the adjacent leg is equal to zero (division by zero is undefined). Therefore, while sine and cosine can describe the ratios of the sides of any right triangle, the tangent ratio is undefined for certain angles.
In summary, while the values of tangent, sine, and cosine are all trigonometric ratios that relate the lengths of sides of a right triangle, the tangent ratio can have a wider range of values and has vertical asymptotes where the adjacent leg is equal to zero, making it undefined for certain angles.