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What is tan(0)?

Question:

What is tan(0)?

The Unit Circle:

In trigonometry, the unit circle is a handy tool that we can use to evaluate trigonometric functions of various angles. This circle has its center at the origin of a graph, and a radius of length 1 unit. Each point on the unit circle has form (cos(θ), sin(θ)), where θ is the angle formed counterclockwise between the positive x-axis and the ray extending from the origin to that point on the circle.

Answer and Explanation: 1

tan(0) = 0

We can calculate this using a trigonometric identity and the unit circle. The identity we will be using is as follows:

  • {eq}tan(\theta )=\frac{sin(\theta )}{cos(\theta )} {/eq}

On the unit circle, the angle θ = 0 corresponds to the point (1,0) as shown in the image.


The Unit Circle


By the definition of the unit circle, we have the following:

  • (1,0) = (cos(0), sin(0))

Therefore, we have that cos(0) = 1 and sin(0) = 0. Plugging these into our trigonometric identity for tan(0), we get the following:

  • {eq}tan(0)=\frac{sin(0)}{cos(0)}=\frac{0}{1}=0 {/eq}

All together, this gives that tan(0) = 0.


Learn more about this topic:

Radians & Degrees on the Unit Circle
Radians & Degrees on the Unit Circle

from

Chapter 26 / Lesson 12
18K

Angles are important in all kinds of fields, such as construction, science, math, navigation, and engineering. There are two units that we can use to measure angles: degrees and radians. In this lesson, learn how to use these units and how they are related to the unit circle.


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