Answer to Question #155812 in Calculus for Jhocel Mae

Question

Hello I need answers, solution and further explanation with regards to these problems, I hope you'll be able to help me again, I really had a hard time solving these.

A.     Find the least positive and the greatest negative coterminal angles of the following angle measures.

1.   -25 degree

2.   110 degree

3.11pie/6 radians

4.    -5 pie/4 radians

B.   Find the angle between 0 degree and 360 degree (if in degrees) or between 0 rad and 2pie rad (if in radians) that is coterminal with the given angle.

5.   -420 degree

6.    5pie/4 radians

7.   60 degree

C.   Find the angle between -360degree and 0 degree (if in degrees) or between -2pie rad and 0 rad (if in radians ) that is coterminal with the given angle.

8.   150 degree

9.    -11 pie/6 radians

10.-45 degree

Answer 1

Coterminal basically are angles with the same initials and terminals.

When solving problems of coterminal angles, it is always advisable to draw out the given angles.

A.     Find the least positive and the greatest negative coterminal angles of the following angle measures.

1.   -25 degree

least positive coterminal angle$= -25^o +360^o =335^o$

Greatest negative coterminal angle $= -25^o -360^o=-385^o$

2.   110 degree

least positive coterminal angle$= 110^o +360^o =470^o$

Greatest negative coterminal angle $= 110^o -360^o=-250^o$

3. ${11\pi \over 6}rad$

least positive coterminal angle$= {11\pi \over 6}rad +2\pi rad ={23\pi \over 6} rad$

Greatest negative coterminal angle $={11\pi \over 6}rad -2\pi=-{\pi \over 6}rad$

4.   $-{5\pi \over 4}rad$

least positive coterminal angle$=-{5\pi \over 4}rad +2\pi rad ={3\pi \over 4} rad$

Greatest negative coterminal angle $=-{5\pi \over 4}rad -2\pi=-{13\pi \over 4}rad$

B.   Find the angle between 0 degree and 360 degree (if in degrees) or between 0 rad and 2pie rad (if in radians) that is coterminal with the given angle.

Since it is between 0 and 360 degree, the are asking for the least positive coterminal angle

5.   -420 degree

least positive coterminal angle$= -420^o +720^o =300^o$

6.    5pie/4 radians

least positive coterminal angle$={5\pi \over 4}rad +2\pi rad ={13\pi \over 4} rad$

7.   60 degree

least positive coterminal angle$= 60^o +360^o =420^o$

C.   Find the angle between -360degree and 0 degree (if in degrees) or between -2pie rad and 0 rad (if in radians ) that is coterminal with the given angle.

Since it is between -360 and 0 degree, they are asking for the greatest negative coterminal angle

8.   150 degree

greatest negative coterminal angle$= 150^o -360^o =-210^o$

9.  $-{11\pi \over 6}rad$

greatest negative coterminal angle$= -{11\pi \over 6}rad -2\pi rad =-{23\pi \over 6} rad$

10.-45 degree

greatest negative coterminal angle$= -45^o -360^o =-405^o$