The coterminal angle of -15π/4 can be found by adding or subtracting a multiple of 2π (or 360°) to the given angle.
To find the coterminal angle, we can add 2π to -15π/4:
-15π/4 + 2π
Simplifying, we can convert -15π/4 to an improper fraction:
-15π/4 = -15π/4 * 4/4 = -60π/4
Now we add 2π to get the coterminal angle:
-60π/4 + 2π = -60π/4 + 8π/4 = -52π/4
Simplifying further:
-52π/4 = -13π/1 = -13π
So, the coterminal angle of -15π/4 is -13π.
Another way to find the coterminal angle is to subtract 2π from -15π/4:
-15π/4 - 2π = -15π/4 - 8π/4 = -23π/4
Simplifying:
-23π/4 = -5π/1 = -5π
Therefore, another coterminal angle of -15π/4 is -5π.
In summary, the coterminal angles of -15π/4 are -13π and -5π.