find tan 0
Understand the Problem
The question is asking for the value of the tangent function at 0 degrees or 0 radians. To solve this, we will use the basic properties of trigonometric functions.
Answer
The value of $\tan(0)$ is $0$.
Answer for screen readers
The value of $\tan(0)$ is $0$.
Steps to Solve
- Identify the tangent function The tangent function is defined as the ratio of the sine function to the cosine function. Therefore, we can express the tangent of an angle $\theta$ as:
$$ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $$
- Substitute the angle with 0 For our specific case, we want to find $\tan(0)$, so we substitute $\theta$ with 0:
$$ \tan(0) = \frac{\sin(0)}{\cos(0)} $$
- Evaluate sine and cosine at 0 Now we need the values of $\sin(0)$ and $\cos(0)$:
- We know that $\sin(0) = 0$
- We also know that $\cos(0) = 1$
- Calculate the tangent value Substituting these values into the tangent equation, we have:
$$ \tan(0) = \frac{0}{1} = 0 $$
The value of $\tan(0)$ is $0$.
More Information
The tangent function measures the slope of the line formed by the angle in a right triangle. At 0 degrees (or 0 radians), the angle corresponds to the "flat" case, where there is no rise over run, hence the tangent value is 0.
Tips
One common mistake is to confuse the values of sine and cosine at the angle of 0. Always remember that $\sin(0) = 0$ and $\cos(0) = 1$.
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