There are several ways to solve this question, however, we will be opting to prove this statement through the General Method.
As stated in the question, the limit of sinx/x as x→0 can be calculated through a few basic steps that involve basic knowledge of the shape of the trigonometric functions.
Since we are aware that x is ultimately going to equal 0, so if we substitute the value of x=0 in the sinx function, we know that sin(0) would equal 0 as well. However, we also know that x=0, so we can replace the 0 in the numerator with x, hence transforming the equation to x/x. Now we are aware that any number or variable divided by itself equals 1, so as x→0, the limit of sinx/x approaches 1.
