The tangent of 0 degrees, or tan(0), is 0.
Understanding Tangent
The tangent function (tan) in trigonometry represents the ratio of the opposite side to the adjacent side of a right-angled triangle. It can also be defined as the sine of an angle divided by its cosine: tan(θ) = sin(θ) / cos(θ).
At 0 degrees, the opposite side of the right-angled triangle has a length of 0, while the adjacent side has a length greater than 0. Therefore, the ratio becomes 0/x (where x is the length of the adjacent side), which equals 0.
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Visual Representation: Imagine a unit circle. As the angle approaches 0, the slope of the line connecting the origin to the point on the circle approaches 0. The slope represents the tangent of the angle.
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Formulaic Approach: Using the formula tan(θ) = sin(θ) / cos(θ), we know that sin(0) = 0 and cos(0) = 1. Thus, tan(0) = 0/1 = 0.
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Practical Applications: The tangent function is crucial in various fields, including:
- Engineering: Calculating slopes and gradients.
- Physics: Analyzing projectile motion and oscillations.
- Computer Graphics: Representing rotations and transformations.
Multiple sources confirm this:
- cuemath.com: Explicitly states that the value of tan 0 degrees is 0.
- Byjus.com: Defines the tangent function as the ratio of opposite to adjacent sides and concludes that tan 0 degrees is 0.
- Vedantu.com: Shows the derivation, tan 0° = sin 0° / cos 0° = 0/1 = 0.
- Mathway.com: Provides the answer as 0.
