Solution 4.1:2
From Förberedande kurs i matematik 1
(Difference between revisions)
m (Robot: Automated text replacement (-[[Bild: +[[Image:)) |
m |
||
(2 intermediate revisions not shown.) | |||
Line 1: | Line 1: | ||
- | {{ | + | If we use the mnemonic that one turn is 360° or <math>2\pi</math> radians, we can derive a formula for the transformation from degrees to radians. Because |
- | < | + | |
- | {{ | + | {{Displayed math||<math>360\cdot 1^{\circ } = 2\pi\ \text{radians}</math>}} |
+ | |||
+ | this gives | ||
+ | |||
+ | {{Displayed math||<math>1^{\circ} = \frac{2\pi}{360}\ \text{radians} = \frac{\pi}{180}\ \text{radians.}</math>}} | ||
+ | |||
+ | Now we can start transforming the angles: | ||
+ | |||
+ | |||
+ | {| | ||
+ | ||a) | ||
+ | |width="100%"|<math>45^{\circ} = 45\cdot 1^{\circ} = 45\cdot\frac{\pi}{180}\ \text{radians} = \frac{\pi}{4}\ \text{radians,}</math> | ||
+ | |- | ||
+ | |height="10px"| | ||
+ | |- | ||
+ | ||b) | ||
+ | |width="100%"|<math>135^{\circ } = 135\cdot 1^{\circ} = 135\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{4}\ \text{radians,}</math> | ||
+ | |- | ||
+ | |height="10px"| | ||
+ | |- | ||
+ | ||c) | ||
+ | |width="100%"|<math>-63^{\circ} = -63\cdot 1^{\circ} = -63\cdot\frac{\pi}{180}\ \text{radians} = -\frac{7\pi}{20}\ \text{radians,}</math> | ||
+ | |- | ||
+ | |height="10px"| | ||
+ | |- | ||
+ | ||d) | ||
+ | |width="100%"|<math>270^{\circ} = 270\cdot 1^{\circ} = 270\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{2}\ \text{radians.}</math> | ||
+ | |} |
Current revision
If we use the mnemonic that one turn is 360° or \displaystyle 2\pi radians, we can derive a formula for the transformation from degrees to radians. Because
\displaystyle 360\cdot 1^{\circ } = 2\pi\ \text{radians} |
this gives
\displaystyle 1^{\circ} = \frac{2\pi}{360}\ \text{radians} = \frac{\pi}{180}\ \text{radians.} |
Now we can start transforming the angles:
a) | \displaystyle 45^{\circ} = 45\cdot 1^{\circ} = 45\cdot\frac{\pi}{180}\ \text{radians} = \frac{\pi}{4}\ \text{radians,} |
b) | \displaystyle 135^{\circ } = 135\cdot 1^{\circ} = 135\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{4}\ \text{radians,} |
c) | \displaystyle -63^{\circ} = -63\cdot 1^{\circ} = -63\cdot\frac{\pi}{180}\ \text{radians} = -\frac{7\pi}{20}\ \text{radians,} |
d) | \displaystyle 270^{\circ} = 270\cdot 1^{\circ} = 270\cdot\frac{\pi}{180}\ \text{radians} = \frac{3\pi}{2}\ \text{radians.} |