What does cosx/x and tanx/x represent?

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Thread starter JayCAquino#4
Start date Sep 23, 2015
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Calculus Cosine Tangent Trigonometry

In summary, cosx/x and tanx/x are trigonometric functions divided by the variable x. Their graphs are continuous, non-linear curves with different asymptotes. They are periodic, have a range of all real numbers, and are odd functions. In real-life applications, they are used to model periodic phenomena and calculate distances and angles. As x approaches 0, the limit of both functions is 1.

Sep 23, 2015

JayCAquino#4

What do the functions cosx/x and tanx/x represent?

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Sep 23, 2015

axmls

Depends on the context.

Sep 23, 2015

JayCAquino#4

In terms of the ratios of the sides of triangles

Related to What does cosx/x and tanx/x represent?

1. What is the definition of cosx/x and tanx/x?

Cosx/x and tanx/x represent the trigonometric functions cosine and tangent, respectively, divided by the variable x.

2. What is the graph of cosx/x and tanx/x?

The graph of cosx/x and tanx/x is a continuous, non-linear curve. The graph of cosx/x has a horizontal asymptote at y=1, while the graph of tanx/x has vertical asymptotes at x=0 and x=±π.

3. What are the properties of cosx/x and tanx/x?

The properties of cosx/x and tanx/x include being periodic, having a range of all real numbers, and being odd functions (symmetric about the origin). Additionally, the absolute value of cosx/x is always less than or equal to 1, while the absolute value of tanx/x is always greater than or equal to 1.

4. How are cosx/x and tanx/x used in real-life applications?

Cosx/x and tanx/x are used in various fields such as engineering, physics, and astronomy to model real-world periodic phenomena, such as sound waves and planetary orbits. They are also used in navigation and surveying to calculate distances and angles.

5. What is the limit of cosx/x and tanx/x as x approaches 0?

The limit of cosx/x as x approaches 0 is 1, and the limit of tanx/x as x approaches 0 is 1. This means that as x gets closer and closer to 0, the value of cosx/x and tanx/x approaches 1.