What Are the Properties of Cosine?


Quick Answer

The cosine function has several distinguishing properties. It is an even function, and it is always a real number. It is also a multiple of Pi. It is not necessary for most math students to remember all the properties of cosine. Rather, the two primary properties are that it is an even function and that it has periodicity. These are most important to commit to memory.

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What Are the Properties of Cosine?
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Full Answer

Cosine is always a real number, which means it can be represented on a number line. The cosine function is also always a continuous number, which implies that it can consist of decimals, rational numbers or irrational numbers. The cosine value of zero is one.

Because cosine is an even function, cos(-p) is always equal to cos(p). The other primary property of the cosine function is that it is periodic in nature with a period of 2p. Mathematically, this means that cos(z) = cos(z + 2p). The limit of the cosine function ranges from -1 to 1.

The cosine function is positive in the first and the fourth quadrants, while it is negative in second and third quadrants.

Cosine is an important concept that has application in a wide range of math and science subjects, including trigonometry, calculus and physics.

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