Question

find a coterminal angle with measure $\theta$, where $0^{circ}leq\theta < 360^{circ}$, for each of the following. 43. $390^{circ}$ 44. $460^{circ}$ 45. $720^{circ}$ 46. $810^{circ}$ 47. $1000^{circ}$ 48. $1360^{circ}$ 49. $- 50^{circ}$ 50. $-110^{circ}$

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles differ by a multiple of 360°. To find a coterminal angle $\theta$ in the range $0^{\circ}\leq\theta < 360^{\circ}$, we add or subtract 360° from the given angle.

Step2: Solve for 390°

$390^{\circ}-360^{\circ}=30^{\circ}$

Step3: Solve for 460°

$460^{\circ}-360^{\circ}=100^{\circ}$

Step4: Solve for 720°

$720^{\circ}- 2\times360^{\circ}=0^{\circ}$

Step5: Solve for 810°

$810^{\circ}-2\times360^{\circ}=90^{\circ}$

Step6: Solve for 1000°

$1000^{\circ}-2\times360^{\circ}=280^{\circ}$

Step7: Solve for 1360°

$1360^{\circ}-3\times360^{\circ}=280^{\circ}$

Step8: Solve for - 50°

$-50^{\circ}+360^{\circ}=310^{\circ}$

Step9: Solve for - 110°

$-110^{\circ}+360^{\circ}=250^{\circ}$

Answer:

1. $30^{\circ}$
2. $100^{\circ}$
3. $0^{\circ}$
4. $90^{\circ}$
5. $280^{\circ}$
6. $280^{\circ}$
7. $310^{\circ}$
8. $250^{\circ}$