What are the positive and negative angle measures coterminal with a -70 degree angle?
To find a positive and a negative angle measure coterminal with a -70 degree angle, we need to add or subtract multiples of 360 degrees.
To find the positive angle measure, we add 360 degrees to -70 degrees:
-70 degrees + 360 degrees = 290 degrees
So, 290 degrees is a positive angle measure coterminal with -70 degrees.
To find the negative angle measure, we subtract 360 degrees from -70 degrees:
-70 degrees - 360 degrees = -430 degrees
So, -430 degrees is a negative angle measure coterminal with -70 degrees.
Understanding Coterminal Angles
A coterminal angle is an angle that has the same initial side and terminal side as another angle but possibly a different number of rotations.
To find coterminal angles, you can add or subtract multiples of 360 degrees (for angles in degrees) or 2π (for angles in radians).
In this case, we have a -70-degree angle. To find a positive coterminal angle, we add 360 degrees to the given angle:
-70 + 360 = 290 degrees.
To find a negative coterminal angle, we subtract 360 degrees from the given angle:
-70 - 360 = -430 degrees.
Coterminal angles are important in trigonometry and geometry as they represent angles that have the same position in standard position but may differ in measurement. Being able to identify coterminal angles helps in simplifying calculations and understanding the relationship between angles.
In conclusion, when dealing with coterminal angles, remember to add or subtract multiples of 360 degrees to find angles that share the same initial and terminal sides. This concept is fundamental in trigonometry and helps in exploring the properties of angles in a geometric context.