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4.3 Exercises
From Förberedande kurs i matematik 1
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Revision as of 13:47, 10 September 2008
| Theory | Exercises |
Exercise 4.3:1
Determine the angles 
2
| a) | 5 | b) | 7 | c) | |
Answer | Solution a | Solution b | Solution c
Loading...Exercise 4.3:2
Determine the angles
| a) | | b) | |
Exercise 4.3:3
Suppose that 2
v2
| a) | | b) | −v) |
| c) | | d) |  2−v |
| e) | 2+v | f) | 3+v |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 4.3:4
Suppose that v
| a) | | b) | |
| c) | | d) | |
| e) | v+4 | f) | v−3 |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f
Exercise 4.3:5
Determine
Exercise 4.3:6
| a) | Determine \displaystyle \ \sin{v}\ and \displaystyle \ \tan{v}\ if \displaystyle \ \cos{v}=\displaystyle \frac{3}{4}\ and \displaystyle \ \displaystyle \frac{3\pi}{2} \leq v \leq 2\pi\,. |
| b) | Determine \displaystyle \ \cos{v}\ and \displaystyle \ \tan{v}\ if \displaystyle \ \sin{v}=\displaystyle \frac{3}{10}\ and \displaystyle \,v\, lies in the second quadrant. |
| c) | Determine \displaystyle \ \sin{v}\ and \displaystyle \ \cos{v}\ if \displaystyle \ \tan{v}=3\ and \displaystyle \ \pi \leq v \leq \displaystyle \frac{3\pi}{2}\,. |
Answer | Solution a | Solution b | Solution c
Exercise 4.3:7
Determine \displaystyle \ \sin{(x+y)}\ if
| a) | \displaystyle \sin{x}=\displaystyle \frac{2}{3}\,,\displaystyle \ \sin{y}=\displaystyle \frac{1}{3}\ and \displaystyle \,x\,, \displaystyle \,y\, are angles in the first quadrant. |
| b) | \displaystyle \cos{x}=\displaystyle \frac{2}{5}\,, \displaystyle \ \cos{y}=\displaystyle \frac{3}{5}\ and \displaystyle \,x\,, \displaystyle \,y\, are angles in the first quadrant. |
Exercise 4.3:8
Show the following trigonometric relations
| a) | \displaystyle \tan^2v=\displaystyle\frac{\sin^2v}{1-\sin^2v} |
| b) | \displaystyle \displaystyle \frac{1}{\cos v}-\tan v=\frac{\cos v}{1+\sin v} |
| c) | \displaystyle \tan\displaystyle\frac{u}{2}=\frac{\sin u}{1+\cos u} |
| d) | \displaystyle \displaystyle\frac{\cos (u+v)}{\cos u \cos v}= 1- \tan u \tan v |
Exercise 4.3:9
| Show Feynman's equality | |
| (Hint: use the formula for double angles on \displaystyle \,\sin 160^\circ\,.) |
