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.
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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:

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Chapter 26 / Lesson 12Learn to define what a radian is. Find out what a unit circle is and how many radians are in a circle. Learn to convert between radians and degrees. See examples.