reference angle for tan 420. give me exact answer

To find the reference angle for \(\tan 420^\circ\), follow these steps:

1. **Reduce the angle to within \(0^\circ\) to \(360^\circ\):**
   \[
   420^\circ - 360^\circ = 60^\circ
   \]
   So, \(420^\circ\) is coterminal with \(60^\circ\).

2. **Determine the reference angle:**
   Since \(60^\circ\) is in the first quadrant, the reference angle is simply \(60^\circ\).

The exact reference angle for \(\tan 420^\circ\) is \(60^\circ\).

Would you like to know how to use this reference angle, or do you have any other questions?

Here are 5 related questions:

1. How do you find the reference angle for negative angles?
2. What is the tangent of \(60^\circ\)?
3. How do you find the reference angle for angles greater than \(360^\circ\)?
4. What are coterminal angles?
5. How does the reference angle relate to the unit circle?

**Tip:** For any angle greater than \(360^\circ\), subtract \(360^\circ\) repeatedly until the angle falls within the range \(0^\circ\) to \(360^\circ\).

Discover how to find the exact reference angle for tan 420 degrees step-by-step. Learn the concept of reference angles in trigonometry and how to reduce angles greater than 360 degrees. Suitable for high school students and anyone studying trigonometric functions.

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