How To Find A Coterminal Angle Between 0 And 360
Find A COTERMINAL Angle Betwixt 0° AND 360°
1 consummate rotation of a ray in the anticlockwise direction results in an bending measuring of 360°.
By continuing the anticlockwise rotation, angles larger than 360° can be produced.
If nosotros rotate in clockwise direction, negative angles are produced. Angles 57°,417°and -303°accept the same initial side and terminal side merely with different amount of rotations, such angles are called coterminal angles.
Example :
For each given angle, observe a coterminal angle with measure of θ such that 0° ≤ θ< 360°.
(i) 395° (ii) 525° (iii) 1150°(iv) -270° (v) -450°
Solution :
(i) 395°
Write 395° in terms of 360°.
395° = 360° + 35°
Then, the coterminal angle of 395°is 35◦
(ii) 525°
Write 525°in terms of 360°.
525° = 360° + 165°
So, the coterminal angle of 525° is 165°.
(iii) 1150°
Write 1150° in terms of 360°.
1150° = 3(360°) + 70°
Then, the coterminal bending of 1150° is seventy°.
(iv) -270°
Write -270° in terms of 360°.
-270° = -360° + 90°
So, the coterminal angle of 270° is 90°.
(v) -450°
Write -450° in terms of 360 °.
-450° = -360° - xc°
And so, the coterminal angle of 450° is -90 °.
How to determine the quadrant of an angle ?
Positive Angle Quadrant :
Angle lies betwixt 0° and 90 ° -----> onest quadrant
Bending lies between ninety° and 180° -----> twond quadrant
Angle lies betwixt 180° and 270 ° -----> 3rd quadrant
Bending lies between 270° and 360° -----> 2th quadrant
Negative Bending Quadrant :
Bending lies between 0° and -90° -----> 4 thursday quadrant
Angle lies between -xc ° and -180 ° -----> 3rd quadrant
Angle lies between -180 ° and -270° -----> ii nd quadrant
Angle lies between -270° and -360 ° -----> onest quadrant
Example :
Identify the quadrant in which an angle of each given measure lies
(i) 25° (2) 825° (iii) −55°
Solution :
(i) 25 °
25 ° lies betwixt0° and 90°.
So, 25 ° lies in the first quadrant.
(2) 825°
If the given angle measures more 360°, then nosotros take to divide the given angle by 360 and find the quadrant for the remaining angle.
When 825° is divided by 360°, the remainder is 105°.
105° lies between 90 ° and 180 °.
So, 105 ° lies in the second quadrant.
(i) -55 °
-55 ° lies between -90 ° and 0°.
And so, -v5 ° lies in the fourth quadrant.
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