a positive angle less than 2 pi their is a coterminal 17 pi/4
To find a positive angle that is less than 2π (or 360 degrees) and is coterminal with 17π/4, we can use the fact that angles that differ by a multiple of 2π (or 360 degrees) are coterminal.
First, let's simplify 17π/4. Since π is equivalent to 180 degrees, we have:
17π/4 = 17 * (180 degrees) / 4 = 3060 degrees / 4 = 765 degrees.
Now, since we want to find a positive angle less than 2π (or 360 degrees) that is coterminal with 765 degrees, we can subtract multiples of 360 degrees until we get a positive angle in the desired range.
765 degrees - 360 degrees = 405 degrees
Since 405 degrees is still larger than 360 degrees, we subtract another 360 degrees:
405 degrees - 360 degrees = 45 degrees.
Therefore, a positive angle less than 2π that is coterminal with 17π/4 is 45 degrees.