4.4 Exercises
From Förberedande kurs i matematik 1
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| - | {{Ej vald flik|[[4.4 Trigonometriska ekvationer| | + | {{Ej vald flik|[[4.4 Trigonometriska ekvationer|Theoy]]}} |
| - | {{Vald flik|[[4.4 Övningar| | + | {{Vald flik|[[4.4 Övningar|Exercises]]}} |
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| - | === | + | ===Exercise 4.4:1=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | For which angles <math>\,v\,</math>, where <math>\,0 \leq v\leq 2\pi\,</math>, does | |
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|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 4.4:1|Lösning a |Lösning 4.4:1a|Lösning b |Lösning 4.4:1b|Lösning c |Lösning 4.4:1c|Lösning d |Lösning 4.4:1d|Lösning e |Lösning 4.4:1e|Lösning f |Lösning 4.4:1f|Lösning g |Lösning 4.4:1g}} | </div>{{#NAVCONTENT:Svar|Svar 4.4:1|Lösning a |Lösning 4.4:1a|Lösning b |Lösning 4.4:1b|Lösning c |Lösning 4.4:1c|Lösning d |Lösning 4.4:1d|Lösning e |Lösning 4.4:1e|Lösning f |Lösning 4.4:1f|Lösning g |Lösning 4.4:1g}} | ||
| - | === | + | ===Exercise 4.4:2=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Solve the equation | |
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|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 4.4:2|Lösning a |Lösning 4.4:2a|Lösning b |Lösning 4.4:2b|Lösning c |Lösning 4.4:2c|Lösning d |Lösning 4.4:2d|Lösning e |Lösning 4.4:2e|Lösning f |Lösning 4.4:2f}} | </div>{{#NAVCONTENT:Svar|Svar 4.4:2|Lösning a |Lösning 4.4:2a|Lösning b |Lösning 4.4:2b|Lösning c |Lösning 4.4:2c|Lösning d |Lösning 4.4:2d|Lösning e |Lösning 4.4:2e|Lösning f |Lösning 4.4:2f}} | ||
| - | === | + | ===Exercise 4.4:3=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Solve the equation | |
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|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 4.4:3|Lösning a |Lösning 4.4:3a|Lösning b |Lösning 4.4:3b|Lösning c |Lösning 4.4:3c|Lösning d |Lösning 4.4:3d}} | </div>{{#NAVCONTENT:Svar|Svar 4.4:3|Lösning a |Lösning 4.4:3a|Lösning b |Lösning 4.4:3b|Lösning c |Lösning 4.4:3c|Lösning d |Lösning 4.4:3d}} | ||
| - | === | + | ===Exercise 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>. | |
</div>{{#NAVCONTENT:Svar|Svar 4.4:4|Lösning |Lösning 4.4:4}} | </div>{{#NAVCONTENT:Svar|Svar 4.4:4|Lösning |Lösning 4.4:4}} | ||
| - | === | + | ===Exercise 4.4:5=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Solve the equation | |
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|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 4.4:5|Lösning a |Lösning 4.4:5a|Lösning b |Lösning 4.4:5b|Lösning c |Lösning 4.4:5c}} | </div>{{#NAVCONTENT:Svar|Svar 4.4:5|Lösning a |Lösning 4.4:5a|Lösning b |Lösning 4.4:5b|Lösning c |Lösning 4.4:5c}} | ||
| - | === | + | ===Exercise 4.4:6=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Solve the equation | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 4.4:6|Lösning a |Lösning 4.4:6a|Lösning b |Lösning 4.4:6b|Lösning c |Lösning 4.4:6c}} | </div>{{#NAVCONTENT:Svar|Svar 4.4:6|Lösning a |Lösning 4.4:6a|Lösning b |Lösning 4.4:6b|Lösning c |Lösning 4.4:6c}} | ||
| - | === | + | ===Exercise 4.4:7=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Solve the equation | |
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|a) | |a) | ||
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</div>{{#NAVCONTENT:Svar|Svar 4.4:7|Lösning a |Lösning 4.4:7a|Lösning b |Lösning 4.4:7b|Lösning c |Lösning 4.4:7c}} | </div>{{#NAVCONTENT:Svar|Svar 4.4:7|Lösning a |Lösning 4.4:7a|Lösning b |Lösning 4.4:7b|Lösning c |Lösning 4.4:7c}} | ||
| - | === | + | ===Exercise 4.4:8=== |
<div class="ovning"> | <div class="ovning"> | ||
| - | + | Solve the equation | |
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
|a) | |a) | ||
Revision as of 18:21, 3 August 2008
| Theoy | Exercises |
Exercise 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}} |
Svar
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Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning f
Lösning g
Exercise 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}} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning f
Exercise 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} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Exercise 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}\,.
Svar
Lösning
Exercise 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) |
Exercise 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 |
Exercise 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} |
Exercise 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} |
