What is the value of tan(0)?
Understand the Problem
The question is asking for the value of the tangent function at an angle of 0 degrees. To find this, we can refer to the properties of trigonometric functions.
Answer
The value of tangent at 0 degrees is $0$.
Answer for screen readers
The value of the tangent function at 0 degrees is $0$.
Steps to Solve
- Identify the angle in radians
Since trigonometric functions often use radians, convert the angle from degrees to radians. The formula for conversion is:
$$ \text{radians} = \text{degrees} \times \frac{\pi}{180} $$
For 0 degrees:
$$ 0 \times \frac{\pi}{180} = 0 , \text{radians} $$
- Apply the tangent function
The tangent function is defined as the ratio of the sine function to the cosine function:
$$ \tan(x) = \frac{\sin(x)}{\cos(x)} $$
Substituting $x = 0$ radians:
$$ \tan(0) = \frac{\sin(0)}{\cos(0)} $$
- Calculate sine and cosine at 0 radians
We know that:
$$ \sin(0) = 0 $$
$$ \cos(0) = 1 $$
- Evaluate the tangent function
Now, substitute the values of sine and cosine back into the tangent equation:
$$ \tan(0) = \frac{0}{1} = 0 $$
The value of the tangent function at 0 degrees is $0$.
More Information
The tangent function is one of the fundamental trigonometric functions and it is especially important in various applications, such as physics and engineering. At 0 degrees (or 0 radians), the tangent equals zero, which corresponds to the point on the unit circle where the angle intersects the x-axis.
Tips
- Confusing radians and degrees: Always ensure you are using the correct unit. It's helpful to convert degrees to radians when needed.
- Misunderstanding tangent's definition: Remember that tangent is the ratio of sine to cosine, and that accurate values for sine and cosine are crucial for finding tangent.
