What is the value of tan 30 degrees?
Understand the Problem
The question is asking for the value of the tangent of 30 degrees, which is a standard trigonometric value.
Answer
The value of $\tan(30^\circ)$ is $\frac{1}{\sqrt{3}}$ or $\frac{\sqrt{3}}{3}$.
Answer for screen readers
The value of $\tan(30^\circ)$ is $\frac{1}{\sqrt{3}}$ or equivalently $\frac{\sqrt{3}}{3}$.
Steps to Solve
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Identify the Tangent Function The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. For angle $\theta$, it is expressed as: $$ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} $$
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Use the Known Value for Tangent of 30 Degrees The value of the tangent function for standard angles is often memorized. $\tan(30^\circ)$ has a known value: $$ \tan(30^\circ) = \frac{1}{\sqrt{3}} $$
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Rationalize the Denominator (Optional) To express the value in a more simplified form without a square root in the denominator, you can multiply the numerator and denominator by $\sqrt{3}$: $$ \tan(30^\circ) = \frac{1 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{\sqrt{3}}{3} $$
The value of $\tan(30^\circ)$ is $\frac{1}{\sqrt{3}}$ or equivalently $\frac{\sqrt{3}}{3}$.
More Information
The tangent of 30 degrees is a commonly used trigonometric value, especially in problems related to right triangles. It's derived from the angles in a 30-60-90 triangle, where the ratios of the sides are well established.
Tips
- Confusing the values for $\tan(30^\circ)$ and $\tan(45^\circ)$; remember that $\tan(45^\circ) = 1$.
- Forgetting to simplify or rationalize the denominator when dealing with radical expressions.
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