What is the Difference Between Sin and Cos?

The main difference between sine (sin) and cosine (cos) lies in their definitions and applications within right triangles. In a right-angled triangle, they are both trigonometric functions that describe the ratio of two sides:

• Sine (sin): The sine of an angle (θ) is the ratio of the length of the opposite side to the hypotenuse (the side opposite the angle). In other words, sin(θ) = opposite / hypotenuse.
• Cosine (cos): The cosine of an angle (θ) is the ratio of the length of the adjacent side to the hypotenuse (the side next to the angle). In other words, cos(θ) = adjacent / hypotenuse.

Another difference between the two functions is their relationship with complementary angles. The sine of an angle is equal to the cosine of its complementary angle, and vice versa. For example, sin(x°) = cos(90° - x°), and cos(x°) = sin(90° - x°).

In terms of graphical representation, the graphs of sine and cosine functions are different. The cosine function is the same as the sine function but shifted to the left by 90 degrees. This means that they have the same shape but are shifted relative to each other on the coordinate axes.

Comparative Table: Sin vs Cos

The main difference between sine and cosine functions lies in their relationships with the angles in a right-angled triangle. Here is a table summarizing the differences between sine and cosine:

Some additional differences between sine and cosine functions include:

• The sine function has a period of $$2\pi$$, while the cosine function has a period of $$2\pi$$ as well.
• The range of both sine and cosine functions is $$[-1, 1]$$, as they are defined for all real numbers.
• The graphs of the sine and cosine functions are shifted by 90 degrees from each other, with the cosine function being the shifted version of the sine function.