4.2 Übungen

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===Exercise 4.2:1===
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===Übung 4.2:1===
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Using the trigonometric functions, determine the length of the side marked<math>\,x\,</math>
Using the trigonometric functions, determine the length of the side marked<math>\,x\,</math>
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</div>{{#NAVCONTENT:Answer|Answer 4.2:1|Solution a |Solution 4.2:1a|Solution b |Solution 4.2:1b|Solution c |Solution 4.2:1c|Solution d |Solution 4.2:1d|Solution e |Solution 4.2:1e|Solution f |Solution 4.2:1f}}
</div>{{#NAVCONTENT:Answer|Answer 4.2:1|Solution a |Solution 4.2:1a|Solution b |Solution 4.2:1b|Solution c |Solution 4.2:1c|Solution d |Solution 4.2:1d|Solution e |Solution 4.2:1e|Solution f |Solution 4.2:1f}}
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===Exercise 4.2:2===
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===Übung 4.2:2===
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Determine a trigonometric equation that is satisfied by <math>\,v\,</math>.
Determine a trigonometric equation that is satisfied by <math>\,v\,</math>.
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</div>{{#NAVCONTENT:Answer|Answer 4.2:2|Solution a |Solution 4.2:2a|Solution b |Solution 4.2:2b|Solution c |Solution 4.2:2c|Solution d |Solution 4.2:2d|Solution e |Solution 4.2:2e|Solution f |Solution 4.2:2f}}
</div>{{#NAVCONTENT:Answer|Answer 4.2:2|Solution a |Solution 4.2:2a|Solution b |Solution 4.2:2b|Solution c |Solution 4.2:2c|Solution d |Solution 4.2:2d|Solution e |Solution 4.2:2e|Solution f |Solution 4.2:2f}}
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===Exercise 4.2:3===
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===Übung 4.2:3===
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Determine
Determine
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</div>{{#NAVCONTENT:Answer|Answer 4.2:3|Solution a |Solution 4.2:3a|Solution b |Solution 4.2:3b|Solution c |Solution 4.2:3c|Solution d |Solution 4.2:3d|Solution e |Solution 4.2:3e|Solution f |Solution 4.2:3f}}
</div>{{#NAVCONTENT:Answer|Answer 4.2:3|Solution a |Solution 4.2:3a|Solution b |Solution 4.2:3b|Solution c |Solution 4.2:3c|Solution d |Solution 4.2:3d|Solution e |Solution 4.2:3e|Solution f |Solution 4.2:3f}}
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===Exercise 4.2:4===
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===Übung 4.2:4===
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Determine
Determine
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</div>{{#NAVCONTENT:Answer|Answer 4.2:4|Solution a |Solution 4.2:4a|Solution b |Solution 4.2:4b|Solution c |Solution 4.2:4c|Solution d |Solution 4.2:4d|Solution e |Solution 4.2:4e|Solution f |Solution 4.2:4f}}
</div>{{#NAVCONTENT:Answer|Answer 4.2:4|Solution a |Solution 4.2:4a|Solution b |Solution 4.2:4b|Solution c |Solution 4.2:4c|Solution d |Solution 4.2:4d|Solution e |Solution 4.2:4e|Solution f |Solution 4.2:4f}}
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===Exercise 4.2:5===
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===Übung 4.2:5===
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Determine
Determine
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</div>{{#NAVCONTENT:Answer|Answer 4.2:5|Solution a |Solution 4.2:5a|Solution b |Solution 4.2:5b|Solution c |Solution 4.2:5c|Solution d |Solution 4.2:5d}}
</div>{{#NAVCONTENT:Answer|Answer 4.2:5|Solution a |Solution 4.2:5a|Solution b |Solution 4.2:5b|Solution c |Solution 4.2:5c|Solution d |Solution 4.2:5d}}
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===Exercise 4.2:6===
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===Übung 4.2:6===
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Determine the length of the side marked <math>\,x\,</math>.
Determine the length of the side marked <math>\,x\,</math>.
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</div>{{#NAVCONTENT:Answer|Answer 4.2:6|Solution |Solution 4.2:6}}
</div>{{#NAVCONTENT:Answer|Answer 4.2:6|Solution |Solution 4.2:6}}
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===Exercise 4.2:7===
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===Übung 4.2:7===
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In order to determine the width of a river, we measure from two points, A and B on one side of the straight bank to a tree, C, on the opposite side. How wide is the river if the measurements in the figure are correct?
In order to determine the width of a river, we measure from two points, A and B on one side of the straight bank to a tree, C, on the opposite side. How wide is the river if the measurements in the figure are correct?
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</div>{{#NAVCONTENT:Answer|Answer 4.2:7|Solution |Solution 4.2:7}}
</div>{{#NAVCONTENT:Answer|Answer 4.2:7|Solution |Solution 4.2:7}}
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===Exercise 4.2:8===
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===Übung 4.2:8===
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A rod of length <math>\,\ell\,</math> hangs from two ropes of length <math>\,a\,</math> and <math>\,b\,</math> as shown in the figure. The ropes make angles <math>\,\alpha\,</math> and <math>\,\beta\,</math> with the vertical. Determine a trigonometric equation
A rod of length <math>\,\ell\,</math> hangs from two ropes of length <math>\,a\,</math> and <math>\,b\,</math> as shown in the figure. The ropes make angles <math>\,\alpha\,</math> and <math>\,\beta\,</math> with the vertical. Determine a trigonometric equation
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</div>{{#NAVCONTENT:Answer|Answer 4.2:8|Solution |Solution 4.2:8}}
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===Exercise 4.2:9===
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===Übung 4.2:9===
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The road from ''A'' to ''B'' consists of three straight parts ''AP'', ''PQ'' and ''QB'', which are 4.0 km, 12.0 km and 5.0 km respectively. The angles marked at ''P'' and ''Q'' in the figure are 30° and 90° respectively. Calculate the distance as the crow flies from ''A'' to ''B''. (The exercise is taken from the Swedish National Exam in Mathematics, November 1976, although slightly modified.)
The road from ''A'' to ''B'' consists of three straight parts ''AP'', ''PQ'' and ''QB'', which are 4.0 km, 12.0 km and 5.0 km respectively. The angles marked at ''P'' and ''Q'' in the figure are 30° and 90° respectively. Calculate the distance as the crow flies from ''A'' to ''B''. (The exercise is taken from the Swedish National Exam in Mathematics, November 1976, although slightly modified.)

Version vom 09:15, 22. Okt. 2008

 

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Übung 4.2:1

Using the trigonometric functions, determine the length of the side marked\displaystyle \,x\,

a)

[Image]

b)

[Image]

c)

[Image]

d)

[Image]

e)

[Image]

f)

[Image]

Answer
Answer 4.2:1
Solution a
Solution 4.2:1a
Solution b
Solution 4.2:1b
Solution c
Solution 4.2:1c
Solution d
Solution 4.2:1d
Solution e
Solution 4.2:1e
Solution f
Solution 4.2:1f

Übung 4.2:2

Determine a trigonometric equation that is satisfied by \displaystyle \,v\,.

a)

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b)

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c)

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d)

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e)

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f)

[Image]

Answer
Answer 4.2:2
Solution a
Solution 4.2:2a
Solution b
Solution 4.2:2b
Solution c
Solution 4.2:2c
Solution d
Solution 4.2:2d
Solution e
Solution 4.2:2e
Solution f
Solution 4.2:2f

Übung 4.2:3

Determine

a) \displaystyle \sin{\left(-\displaystyle \frac{\pi}{2}\right)} b) \displaystyle \cos{2\pi} c) \displaystyle \sin{9\pi}
d) \displaystyle \cos{\displaystyle \frac{7\pi}{2}} e) \displaystyle \sin{\displaystyle \frac{3\pi}{4}} f) \displaystyle \cos{\left(-\displaystyle \frac{\pi}{6}\right)}
Answer
Answer 4.2:3
Solution a
Solution 4.2:3a
Solution b
Solution 4.2:3b
Solution c
Solution 4.2:3c
Solution d
Solution 4.2:3d
Solution e
Solution 4.2:3e
Solution f
Solution 4.2:3f

Übung 4.2:4

Determine

a) \displaystyle \cos{\displaystyle \frac{11\pi}{6}} b) \displaystyle \cos{\displaystyle \frac{11\pi}{3}} c) \displaystyle \tan{\displaystyle \frac{3\pi}{4}}
d) \displaystyle \tan{\pi} e) \displaystyle \tan{\displaystyle \frac{7\pi}{6}} f) \displaystyle \tan{\left(-\displaystyle \frac{5\pi}{3}\right)}
Answer
Answer 4.2:4
Solution a
Solution 4.2:4a
Solution b
Solution 4.2:4b
Solution c
Solution 4.2:4c
Solution d
Solution 4.2:4d
Solution e
Solution 4.2:4e
Solution f
Solution 4.2:4f

Übung 4.2:5

Determine

a) \displaystyle \cos{135^\circ} b) \displaystyle \tan{225^\circ} c) \displaystyle \cos{330^\circ} d) \displaystyle \tan{495^\circ}
Answer
Answer 4.2:5
Solution a
Solution 4.2:5a
Solution b
Solution 4.2:5b
Solution c
Solution 4.2:5c
Solution d
Solution 4.2:5d

Übung 4.2:6

Determine the length of the side marked \displaystyle \,x\,.

[Image]

Answer
Answer 4.2:6
Solution
Solution 4.2:6

Übung 4.2:7

In order to determine the width of a river, we measure from two points, A and B on one side of the straight bank to a tree, C, on the opposite side. How wide is the river if the measurements in the figure are correct?

[Image]

Answer
Answer 4.2:7
Solution
Solution 4.2:7

Übung 4.2:8

A rod of length \displaystyle \,\ell\, hangs from two ropes of length \displaystyle \,a\, and \displaystyle \,b\, as shown in the figure. The ropes make angles \displaystyle \,\alpha\, and \displaystyle \,\beta\, with the vertical. Determine a trigonometric equation for the angle \displaystyle \,\gamma\, which the rod makes with the vertical.

[Image]

Answer
Answer 4.2:8
Solution
Solution 4.2:8

Übung 4.2:9

The road from A to B consists of three straight parts AP, PQ and QB, which are 4.0 km, 12.0 km and 5.0 km respectively. The angles marked at P and Q in the figure are 30° and 90° respectively. Calculate the distance as the crow flies from A to B. (The exercise is taken from the Swedish National Exam in Mathematics, November 1976, although slightly modified.)

[Image]

Answer
Answer 4.2:9
Solution
Solution 4.2:9
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