4.4 Übungen
Aus Online Mathematik Brückenkurs 1
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|width="50%" | <math>\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}</math> | |width="50%" | <math>\tan{v}=-\displaystyle \frac{1}{\sqrt{3}}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:1| | + | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:1|Lösung a |Lösung 4.4:1a|Lösung b |Lösung 4.4:1b|Lösung c |Lösung 4.4:1c|Lösung d |Lösung 4.4:1d|Lösung e |Lösung 4.4:1e|Lösung f |Lösung 4.4:1f|Lösung g |Lösung 4.4:1g}} |
===Übung 4.4:2=== | ===Übung 4.4:2=== | ||
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|width="33%" | <math>\cos{3x}=-\displaystyle\frac{1}{\sqrt{2}}</math> | |width="33%" | <math>\cos{3x}=-\displaystyle\frac{1}{\sqrt{2}}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:2| | + | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:2|Lösung a |Lösung 4.4:2a|Lösung b |Lösung 4.4:2b|Lösung c |Lösung 4.4:2c|Lösung d |Lösung 4.4:2d|Lösung e |Lösung 4.4:2e|Lösung f |Lösung 4.4:2f}} |
===Übung 4.4:3=== | ===Übung 4.4:3=== | ||
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|width="50%" | <math>\sin{3x}=\sin{15^\circ}</math> | |width="50%" | <math>\sin{3x}=\sin{15^\circ}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:3| | + | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:3|Lösung a |Lösung 4.4:3a|Lösung b |Lösung 4.4:3b|Lösung c |Lösung 4.4:3c|Lösung d |Lösung 4.4:3d}} |
===Übung 4.4:4=== | ===Übung 4.4:4=== | ||
<div class="ovning"> | <div class="ovning"> | ||
Determine the angles <math>\,v\,</math> in the interval <math>\,0^\circ \leq v \leq 360^\circ\,</math> which satisfy <math>\ \cos{\left(2v+10^\circ\right)}=\cos{110^\circ}\,</math>. | Determine the angles <math>\,v\,</math> in the interval <math>\,0^\circ \leq v \leq 360^\circ\,</math> which satisfy <math>\ \cos{\left(2v+10^\circ\right)}=\cos{110^\circ}\,</math>. | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:4| | + | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:4|Lösung |Lösung 4.4:4}} |
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|width="50%" | <math>\cos{5x}=\cos(x+\pi/5)</math> | |width="50%" | <math>\cos{5x}=\cos(x+\pi/5)</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:5| | + | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:5|Lösung a |Lösung 4.4:5a|Lösung b |Lösung 4.4:5b|Lösung c |Lösung 4.4:5c}} |
===Übung 4.4:6=== | ===Übung 4.4:6=== | ||
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|width="50%" | <math>\sin 2x = -\sin x</math> | |width="50%" | <math>\sin 2x = -\sin x</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:6| | + | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:6|Lösung a |Lösung 4.4:6a|Lösung b |Lösung 4.4:6b|Lösung c |Lösung 4.4:6c}} |
===Übung 4.4:7=== | ===Übung 4.4:7=== | ||
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|width="50%" | <math>\cos{3x}=\sin{4x}</math> | |width="50%" | <math>\cos{3x}=\sin{4x}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:7| | + | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:7|Lösung a |Lösung 4.4:7a|Lösung b |Lösung 4.4:7b|Lösung c |Lösung 4.4:7c}} |
===Übung 4.4:8=== | ===Übung 4.4:8=== | ||
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|width="50%" | <math>\displaystyle \frac{1}{\cos^2{x}}=1-\tan{x}</math> | |width="50%" | <math>\displaystyle \frac{1}{\cos^2{x}}=1-\tan{x}</math> | ||
|} | |} | ||
| - | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:8| | + | </div>{{#NAVCONTENT:Antwort|Antwort 4.4:8|Lösung a |Lösung 4.4:8a|Lösung b |Lösung 4.4:8b|Lösung c |Lösung 4.4:8c}} |
Version vom 09:31, 22. Okt. 2008
Übung 4.4:1
For which angles \displaystyle \,v\,, where \displaystyle \,0 \leq v\leq 2\pi\,, does
| a) | \displaystyle \sin{v}=\displaystyle \frac{1}{2} | b) | \displaystyle \cos{v}=\displaystyle \frac{1}{2} |
| c) | \displaystyle \sin{v}=1 | d) | \displaystyle \tan{v}=1 |
| e) | \displaystyle \cos{v}=2 | f) | \displaystyle \sin{v}=-\displaystyle \frac{1}{2} |
| g) | \displaystyle \tan{v}=-\displaystyle \frac{1}{\sqrt{3}} |
Antwort
Laden...
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Lösung f
Lösung g
Übung 4.4:2
Solve the equation
| a) | \displaystyle \sin{x}=\displaystyle \frac{\sqrt{3}}{2} | b) | \displaystyle \cos{x}=\displaystyle \frac{1}{2} | c) | \displaystyle \sin{x}=0 |
| d) | \displaystyle \sin{5x}=\displaystyle \frac{1}{\sqrt{2}} | e) | \displaystyle \sin{5x}=\displaystyle \frac{1}{2} | f) | \displaystyle \cos{3x}=-\displaystyle\frac{1}{\sqrt{2}} |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Lösung e
Lösung f
Übung 4.4:3
Solve the equation
| a) | \displaystyle \cos{x}=\cos{\displaystyle \frac{\pi}{6}} | b) | \displaystyle \sin{x}=\sin{\displaystyle \frac{\pi}{5}} |
| c) | \displaystyle \sin{(x+40^\circ)}=\sin{65^\circ} | d) | \displaystyle \sin{3x}=\sin{15^\circ} |
Antwort
Lösung a
Lösung b
Lösung c
Lösung d
Übung 4.4:4
Determine the angles \displaystyle \,v\, in the interval \displaystyle \,0^\circ \leq v \leq 360^\circ\, which satisfy \displaystyle \ \cos{\left(2v+10^\circ\right)}=\cos{110^\circ}\,.
Antwort
Lösung
Übung 4.4:5
Solve the equation
| a) | \displaystyle \sin{3x}=\sin{x} | b) | \displaystyle \tan{x}=\tan{4x} |
| c) | \displaystyle \cos{5x}=\cos(x+\pi/5) |
Übung 4.4:6
Solve the equation
| a) | \displaystyle \sin x\cdot \cos 3x = 2\sin x | b) | \displaystyle \sqrt{2}\sin{x}\cos{x}=\cos{x} |
| c) | \displaystyle \sin 2x = -\sin x |
Übung 4.4:7
Solve the equation
| a) | \displaystyle 2\sin^2{x}+\sin{x}=1 | b) | \displaystyle 2\sin^2{x}-3\cos{x}=0 |
| c) | \displaystyle \cos{3x}=\sin{4x} |
Übung 4.4:8
Solve the equation
| a) | \displaystyle \sin{2x}=\sqrt{2}\cos{x} | b) | \displaystyle \sin{x}=\sqrt{3}\cos{x} |
| c) | \displaystyle \displaystyle \frac{1}{\cos^2{x}}=1-\tan{x} |
