explain how to find the reference angle for 1,406°. Find the reference angle
To find the reference angle for 1,406°, we can follow these steps:
1. Take the given angle and subtract or add multiples of 360° until the resulting angle is between 0° and 360°. This step is necessary because the reference angle is always between 0° and 90°.
Let's subtract 360° from 1,406°:
1,406° - 360° = 1,046°
2. Since 1,046° is still greater than 360°, we need to repeat step 1.
1,046° - 360° = 686°
3. After subtracting another 360°, we have 686°. Repeat step 1.
686° - 360° = 326°
4. Now we have a final angle of 326°, which falls between 0° and 360°.
The reference angle for 1,406° is the acute angle formed between the positive x-axis and the terminal side of 326°. Therefore, the reference angle for 1,406° is 34°.