度数到弧度的转换

角度测量是使用两个不同的系统完成的。六十进制是一个系统，其中一个直角被分成 90 个相等的部分，这些部分被称为度数。每个度数分为 60 个相等的部分，称为分钟，再进一步分为 60 个相等的部分，称为秒。

• 60 秒（或 60”）= 1 分钟（或 1'）
• 90 度（或 90°）= 1 个直角

如何将度数转换为弧度？

解决方案：

Both the degree and the radian in geometry represent the measurement of an angle. 2π (in radians) or 360° can be used to symbolize a complete anticlockwise revolution (in degrees). As a result, the terms degree and radian can be interchanged as follows:

2π radians = 360°

⇒ π radians = 180°

Or, 1° = π/ 180 radians

示例问题

问题一：转换300 ° 为弧度。

解决方案：

We know 180° = π radians = π^c or 1° =  (π/180)^c

Hence, 300° = 300 × π/180 = 5π/3

Thus, 300° = 5π/3 radians

问题2：将35 °转换为弧度。

解决方案：

We know 180° = π radians = π^c or 1° =  (π/180)^c

Hence, 35° = 35 × π/180 = 7π/36

Thus, 35° = 7π/36 radians

问题 3：Convent -56 °到弧度。

解决方案：

We know 180° = π radians = π^c or 1° =  (π/180)^c

Hence, −56° = −56° × π/180 = −14π/45

Thus, −56° = −14π/45 radians

问题 4：将 135 ° 转换为弧度。

解决方案：

We know 180° = π radians = π^c or 1° = (π/180)^c

Hence, 135° = 135 × π/180 = 3π/4

Thus, 135° = 3π/4 radians

问题 5：将 -300 ° 转换为弧度。

解决方案：

We know 180° = π radians = π^c or 1° = (π/180)^c

Hence, −300° = −300 × π/180 = −5π/3

Thus, −300° = −5π/3 radians

问题6：将7 ° 30 ¹转换为弧度。

解决方案：

We know 180° = π radians = π^c or 1° = (π/180)^c

Hence, 7°30¹ = (7 × π/180)^c × (30/60)° = (7½)° × (π/180)^c = (15π/360)^c = π/24

Thus, 7°30¹ = π/24 radians

问题7：将125 ° 30 ¹转换为弧度。

解决方案：

We know 180° = π radians = π^c or 1° = (π/180)^c

Hence, 125°30¹ = 125°(30/60)° = (125½)° = 251π/360

Thus, 125°30¹ = 251π/360 radians

问题8：将-47 ° 30 ¹转换为弧度。

解决方案：

We know 180° = π radians = π^c or 1° =  (π/180)^c

Hence, −47°30¹ = −47°(30/60)° = (−47½)° = (−95/2)° =  (−95/2 × π/180 )° = −19π/72

Thus, −47°30¹ = −19π/72 radians