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4.2 Übungen

Aus Online Mathematik Brückenkurs 1

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Exercise 4.2:1

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

a)	4.2 - Figure - A right-angled triangle with angle 27° and sides x and 13	b)	4.2 - Figure - A right-angled triangle with angle 32° and sides x and 25
c)	4.2 - Figure - A right-angled triangle with angle 40° and sides 14 and x	d)	4.2 - Figure - A right-angled triangle with angle 20° and sides 16 and x
e)	4.2 - Figure - A right-angled triangle with angle 35° and sides 11 and x	f)	4.2 - Figure - A right-angled triangle with angle 50° and sides x and 19

Answer

Solution a

Solution b

Solution c

Solution d

Solution e

Solution f

Exercise 4.2:2

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

a)	4.2 - Figure - A right-angled triangle with angle v and sides 2 and 5	b)	4.2 - Figure - A right-angled triangle with angle v and sides 70 and 110
c)	4.2 - Figure - A right-angled triangle with angle v and sides 5 and 7	d)	4.2 - Figur - Rätvinklig triangel med vinkeln v och sidor 3 och 5
e)	4.2 - Figure - A right-angled triangle with angles v and 60° and side 5	f)	4.2 - Figure - An isosceles triangle with top angle v and sides 2, 3 and 3

Answer

Solution a

Solution b

Solution c

Solution d

Solution e

Solution f

Exercise 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

Exercise 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

Exercise 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

Exercise 4.2:6

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

4.2 - Figure - Two triangles with angles 45° and 60°, respectively, and height difference x

Answer

Answer 4.2:6

Solution

Solution 4.2:6

Exercise 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?

4.2 - Figure - A river

Answer

Answer 4.2:7

Solution

Solution 4.2:7

Exercise 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.

4.2 - Figure - Hanging rod

Answer

Answer 4.2:8

Solution

Solution 4.2:8

Exercise 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.)