The word cosine literally means "the complement of the sine." Write a paragraph explaining how complements of sine and cosine are connected.
I know that the sine and the cosine of complementary angles are the same. but how can i add more details/write a paragraph?
COSINE was originally written "co.sine," short for COMPLEMENTI SINUS:
the sine of the complement. The COSINE of angle AOB is the sine of the
complementary angle (ABO ).
So Your question states it wrong. COMPLEMENTI SINUS does not mean the complement of the sine, it means the sine of the complement. And that, is exactly what it is. The sine of the complementary angle. The -I ending is for possessives
To write a paragraph explaining how complements of sine and cosine are connected, you can start by providing some background information. Explain that in trigonometry, the complement of an angle refers to the angle that, when added to the original angle, forms a right angle (90 degrees). Then, introduce the definitions of sine and cosine. The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse of a right triangle. Similarly, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
Now, you can discuss how the complements of sine and cosine are related. Start by mentioning that since complementary angles form a right angle, their sum is always 90 degrees. Next, explain that when we consider two complementary angles, one angle will have a sine value and the other will have a cosine value. Here comes the connection: the sine of one angle is equal to the cosine of its complement (the other angle), and vice versa.
To elaborate further, you can provide an example. Suppose we have an angle A and its complement angle B. If the sine of angle A is x, then the cosine of angle B will also be x. This is because the sine of angle A represents the ratio of the opposite side to the hypotenuse, and the cosine of angle B represents the ratio of the adjacent side to the hypotenuse, but since the angles are complementary, the sides adjacent and opposite to each angle are the same.
In summary, the complements of sine and cosine are connected through their values in complementary angles. The sine of an angle is equal to the cosine of its complement, and vice versa. This relationship arises because the ratios of the sides in a right triangle remain constant regardless of the angle chosen, as long as the sides are in the same position relative to the angle.