Question

Determine the angle between 0 and 2π that is coterminal with quantity 17 times pi end quantity over 4 periodquantity 9 times pi end quantity over 4 periodquantity 5 times pi end quantity over 4 periodquantity 3 times pi end quantity over 4 periodpi over 4

Answer 1

Answer: π/4

Explanation:

To find the angle that is coterminal with 17π/4 between 0 and 2π, we can add or subtract any multiple of 2π until we get an angle between 0 and 2π.

First, we can simplify 17π/4 by dividing both the numerator and the denominator by 4 to get:

17π/4 = 4π + π/4

So, any angle that is coterminal with 17π/4 is also coterminal with π/4, because adding or subtracting any multiple of 2π to 4π + π/4 will just change the number of full rotations, but won't change the angle between 0 and 2π.

a) To find the angle coterminal with 9π/4, we can simplify it by dividing both the numerator and the denominator by 4 to get:

9π/4 = 2π + π/4

So, any angle that is coterminal with 9π/4 is also coterminal with π/4, because adding or subtracting any multiple of 2π to 2π + π/4 will just change the number of full rotations, but won't change the angle between 0 and 2π.

b) To find the angle coterminal with 5π/4, we can subtract 2π from 17π/4 to get:

17π/4 - 2π = 9π/4

So, any angle that is coterminal with 5π/4 is also coterminal with 9π/4.

c) To find the angle coterminal with 3π/4, we can subtract 2π from 17π/4 twice to get:

17π/4 - 2π - 2π = 5π/4

So, any angle that is coterminal with 3π/4 is also coterminal with 5π/4.

d) To find the angle coterminal with π/4, we don't need to do anything, since we already simplified 17π/4 to π/4 at the beginning.

Therefore, the angle between 0 and 2π that is coterminal with 17π/4 is also coterminal with π/4.

Answer 2

Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360 degrees or 2π to each angle, depending on whether the given angle is in degrees or radians.

The coterminal of a given angle can be solved by

`\theta\pm2\pi n`

To find an angle that is coterminal with the given angle between 0 and 2π, subtract 2π and apply two full rotations to the given angle.