Solution 4.1:1
From Förberedande kurs i matematik 1
(Difference between revisions)
m |
|||
(3 intermediate revisions not shown.) | |||
Line 1: | Line 1: | ||
- | {{ | + | The only thing we really need to remember is that one revolution corresponds to |
- | < | + | 360° or <math>2\pi</math> radians. Then we get: |
- | {{ | + | |
+ | {| | ||
+ | ||a) | ||
+ | |width="100%"|<math>\frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 360^{\circ} = 90^{\circ}</math> and | ||
+ | |- | ||
+ | || | ||
+ | |width="100%"|<math>\frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 2\pi\ \text{radians} = \frac{\pi}{2}\ \text{radians,}</math> | ||
+ | |- | ||
+ | |height="10px"| | ||
+ | |- | ||
+ | ||b) | ||
+ | |width="100%"|<math>\frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 360^{\circ} = 135^{\circ}</math> and | ||
+ | |- | ||
+ | || | ||
+ | ||<math>\frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 2\pi\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}</math> | ||
+ | |- | ||
+ | |height="10px"| | ||
+ | |- | ||
+ | ||c) | ||
+ | |width="100%"|<math>-\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 360^{\circ} = -240^{\circ}</math> and | ||
+ | |- | ||
+ | || | ||
+ | |width="100%"|<math>-\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 2\pi\ \text{radians} = -\frac{4\pi}{3}\ \text{radians,}</math> | ||
+ | |- | ||
+ | |height="10px"| | ||
+ | |- | ||
+ | ||d) | ||
+ | |width="100%"|<math>\frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 360^{\circ} = 2910^{\circ}</math> and | ||
+ | |- | ||
+ | || | ||
+ | |width="100%"|<math>\frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 2\pi\ \text{radians} = \frac{97\pi}{6}\ \text{radians.}</math> | ||
+ | |} |
Current revision
The only thing we really need to remember is that one revolution corresponds to 360° or \displaystyle 2\pi radians. Then we get:
a) | \displaystyle \frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 360^{\circ} = 90^{\circ} and |
\displaystyle \frac{1}{4}\ \text{revolution} = \frac{1}{4}\cdot 2\pi\ \text{radians} = \frac{\pi}{2}\ \text{radians,} | |
b) | \displaystyle \frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 360^{\circ} = 135^{\circ} and |
\displaystyle \frac{3}{8}\ \text{revolution} = \frac{3}{8}\cdot 2\pi\ \text{radians} = \frac{3\pi}{4}\ \text{radians,} | |
c) | \displaystyle -\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 360^{\circ} = -240^{\circ} and |
\displaystyle -\frac{2}{3}\ \text{revolution} = -\frac{2}{3}\cdot 2\pi\ \text{radians} = -\frac{4\pi}{3}\ \text{radians,} | |
d) | \displaystyle \frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 360^{\circ} = 2910^{\circ} and |
\displaystyle \frac{97}{12}\ \text{revolution} = \frac{97}{12}\cdot 2\pi\ \text{radians} = \frac{97\pi}{6}\ \text{radians.} |