Visit BYJU’S to learn the trigonometry formulas, ratios, tables, functions and examples. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse ), and the cosine is. Example 2: Find the exact length of the shadow cast by a 15 ft tree when the angle of elevation of the sun is 60º. It emphasizes that sine and cosine are continuous and defined for all real numbers, so their limits can be found using direct substitution. Solution: Using the formula of the tangent function, we have. Express tan−1 cosx/(1 − sinx ), – π/2 < x < 3π/2 in the simplest form So we can say: tan () sin () cos () That is our first Trigonometric Identity.