What is a positive coterminal angle to 47° that is between 500° and 1000° and a negative coterminal angle to 47° that is between −500° and 0°?
I don't really understand how to do this >.<
just keep adding/subtracting 360°
47+360 = 407+360 = 767°
47-360 = -313 - 360 = -673°
To find positive and negative coterminal angles to 47°, we need to add or subtract multiples of 360° until we get angles within the desired range.
1. Positive coterminal angle:
We start with 47° and add multiples of 360° until we get an angle between 500° and 1000°.
47° + 360° = 407° (not in the desired range)
407° + 360° = 767° (not in the desired range)
767° + 360° = 1127° (not in the desired range)
1127° - 360° = 767° (coterminal angle within the desired range)
So, a positive coterminal angle to 47° that is between 500° and 1000° is 767°.
2. Negative coterminal angle:
We start with 47° and subtract multiples of 360° until we get an angle between -500° and 0°.
47° - 360° = -313° (not in the desired range)
-313° - 360° = -673° (not in the desired range)
-673° - 360° = -1033° (not in the desired range)
-1033° + 360° = -673° (coterminal angle within the desired range)
So, a negative coterminal angle to 47° that is between -500° and 0° is -673°.
Therefore, the positive coterminal angle is 767° and the negative coterminal angle is -673°.
No problem! I'll explain how to find the positive and negative coterminal angles to 47° that satisfy the given conditions.
To find the positive coterminal angle, we need to add or subtract multiples of 360° until we get an angle in the desired range. In this case, we want an angle between 500° and 1000°.
1. Start with the given angle of 47°.
2. Add 360° repeatedly until the angle is greater than or equal to 500°.
47° + 360° = 407°
407° + 360° = 767°
767° + 360° = 1127°
Since 1127° is greater than 1000°, we need to subtract multiples of 360°.
3. Subtract 360° repeatedly until the angle is less than or equal to 1000°.
1127° - 360° = 767°
767° - 360° = 407°
407° - 360° = 47°
Now we have a positive coterminal angle of 47° that is between 500° and 1000°.
To find the negative coterminal angle, we follow the same steps but in the opposite direction.
1. Start with the given angle of 47°.
2. Subtract 360° repeatedly until the angle is less than or equal to 0°.
47° - 360° = -313°
-313° - 360° = -673°
-673° - 360° = -1033°
Since -1033° is less than -500°, we need to add multiples of 360°.
3. Add 360° repeatedly until the angle is greater than or equal to -500°.
-1033° + 360° = -673°
-673° + 360° = -313°
-313° + 360° = 47°
Now we have a negative coterminal angle of 47° that is between -500° and 0°.
So, the positive coterminal angle to 47° that is between 500° and 1000° is 47°, and the negative coterminal angle to 47° that is between -500° and 0° is also 47°.