Explain how to find the reference angle for 1,406°. Find the reference angle.
To find the reference angle for a given angle, you need to determine the acute angle formed between the terminal side of the angle and the x-axis.
1. Start by converting the given angle to its equivalent positive angle within the interval [0°, 360°]. In this case, 1,406° is greater than 360°, so you subtract multiples of 360° until the result is between 0° and 360°.
1,406° - 4 * 360° = 1,406° - 1,440° = -34°
2. Since the given angle of -34° is negative, we need to find the equivalent positive angle by adding 360°.
-34° + 360° = 326°
3. Now, we have the positive equivalent angle within the interval [0°, 360°], which is 326°.
4. Next, find the reference angle. To do this, subtract the positive equivalent angle from 180°.
180° - 326° = -146°
5. Finally, change the negative angle to a positive angle by taking its absolute value.
||-146°|| = 146°
Therefore, the reference angle for 1,406° is 146°.