Math  /  Trigonometry

QuestionIn Exercises 9-16, convert from DMS to radians.
9. 6060^{\circ}
10. 9090^{\circ}
11. 120120^{\circ}
12. 150150^{\circ}
13. 71.7271.72^{\circ}
14. 11.8311.83^{\circ}
15. 612461^{\circ} 24^{\prime}
16. 753075^{\circ} 30^{\prime}

Studdy Solution
将小数形式的度数转换为弧度,使用公式:
弧度=小数形式的度数×π180 \text{弧度} = \text{小数形式的度数} \times \frac{\pi}{180}
具体解答如下:
9. 6060^{\circ}:
弧度=60×π180=π3 \text{弧度} = 60 \times \frac{\pi}{180} = \frac{\pi}{3}
10. 9090^{\circ}:
弧度=90×π180=π2 \text{弧度} = 90 \times \frac{\pi}{180} = \frac{\pi}{2}
11. 120120^{\circ}:
弧度=120×π180=2π3 \text{弧度} = 120 \times \frac{\pi}{180} = \frac{2\pi}{3}
12. 150150^{\circ}:
弧度=150×π180=5π6 \text{弧度} = 150 \times \frac{\pi}{180} = \frac{5\pi}{6}
13. 71.7271.72^{\circ}:
弧度=71.72×π1801.251弧度 \text{弧度} = 71.72 \times \frac{\pi}{180} \approx 1.251 \text{弧度}
14. 11.8311.83^{\circ}:
弧度=11.83×π1800.206弧度 \text{弧度} = 11.83 \times \frac{\pi}{180} \approx 0.206 \text{弧度}
15. 612461^{\circ} 24^{\prime}:
度数=61+2460=61.4 \text{度数} = 61 + \frac{24}{60} = 61.4 弧度=61.4×π1801.072弧度 \text{弧度} = 61.4 \times \frac{\pi}{180} \approx 1.072 \text{弧度}
16. 753075^{\circ} 30^{\prime}:
度数=75+3060=75.5 \text{度数} = 75 + \frac{30}{60} = 75.5 弧度=75.5×π1801.318弧度 \text{弧度} = 75.5 \times \frac{\pi}{180} \approx 1.318 \text{弧度}

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