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4.2 Übungen

Aus Online Mathematik Brückenkurs 1

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Übung 4.2:1

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

a)		b)
c)		d)
e)		f)

Answer

Solution a

Solution b

Solution c

Solution d

Solution e

Solution f

Übung 4.2:2

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

a)		b)
c)		d)
e)		f)

Answer

Solution a

Solution b

Solution c

Solution d

Solution e

Solution f

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

Solution a

Solution b

Solution c

Solution d

Solution e

Solution f

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

Solution a

Solution b

Solution c

Solution d

Solution e

Solution f

Übung 4.2:5

Determine

\displaystyle \cos{135^\circ}

\displaystyle \tan{225^\circ}

\displaystyle \cos{330^\circ}

\displaystyle \tan{495^\circ}

Answer

Solution a

Solution b

Solution c

Solution d

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.)