4.4 Exercises
From Förberedande kurs i matematik 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> | ||
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| - | </div>{{#NAVCONTENT:Answer|Answer 4.4:1|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.4:1|Solution a |Solution 4.4:1a|Solution b |Solution 4.4:1b|Solution c |Solution 4.4:1c|Solution d |Solution 4.4:1d|Solution e |Solution 4.4:1e|Solution f |Solution 4.4:1f|Solution g |Solution 4.4:1g}} |
===Exercise 4.4:2=== | ===Exercise 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:Answer|Answer 4.4:2|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.4:2|Solution a |Solution 4.4:2a|Solution b |Solution 4.4:2b|Solution c |Solution 4.4:2c|Solution d |Solution 4.4:2d|Solution e |Solution 4.4:2e|Solution f |Solution 4.4:2f}} |
===Exercise 4.4:3=== | ===Exercise 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:Answer|Answer 4.4:3|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.4:3|Solution a |Solution 4.4:3a|Solution b |Solution 4.4:3b|Solution c |Solution 4.4:3c|Solution d |Solution 4.4:3d}} |
===Exercise 4.4:4=== | ===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>. | 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:Answer|Answer 4.4:4|Solution | | + | </div>{{#NAVCONTENT:Answer|Answer 4.4:4|Solution |Solution 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:Answer|Answer 4.4:5|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.4:5|Solution a |Solution 4.4:5a|Solution b |Solution 4.4:5b|Solution c |Solution 4.4:5c}} |
===Exercise 4.4:6=== | ===Exercise 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:Answer|Answer 4.4:6|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.4:6|Solution a |Solution 4.4:6a|Solution b |Solution 4.4:6b|Solution c |Solution 4.4:6c}} |
===Exercise 4.4:7=== | ===Exercise 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:Answer|Answer 4.4:7|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.4:7|Solution a |Solution 4.4:7a|Solution b |Solution 4.4:7b|Solution c |Solution 4.4:7c}} |
===Exercise 4.4:8=== | ===Exercise 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:Answer|Answer 4.4:8|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.4:8|Solution a |Solution 4.4:8a|Solution b |Solution 4.4:8b|Solution c |Solution 4.4:8c}} |
Revision as of 11:22, 9 September 2008
| Theory | 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}} |
Answer
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Solution a
Solution b
Solution c
Solution d
Solution e
Solution f
Solution 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}} |
Answer
Solution a
Solution b
Solution c
Solution d
Solution e
Solution 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} |
Answer
Solution a
Solution b
Solution c
Solution 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}\,.
Answer
Solution
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) |
Answer
Solution a
Solution b
Solution c
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 |
Answer
Solution a
Solution b
Solution c
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} |
Answer
Solution a
Solution b
Solution c
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} |
Answer
Solution a
Solution b
Solution c
