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4.4 Exercises

From Förberedande kurs i matematik 1

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Exercise 4.4:1

For which angles v, where 0v2, does

a) sinv=21 b) cosv=21
c) sinv=1 d) tanv=1
e) cosv=2 f) sinv=−21
g) tanv=−13

Svar | Lösning a | Lösning b | Lösning c | Lösning d | Lösning e | Lösning f | Lösning g

Exercise 4.4:2

Solve the equation

a) sinx=23  b) cosx=21 c) sinx=0
d) sin5x=12 e) sin5x=21 f) cos3x=−12

Svar | Lösning a | Lösning b | Lösning c | Lösning d | Lösning e | Lösning f

Exercise 4.4:3

Solve the equation

a) cosx=cos6 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}

Svar | Lösning a | Lösning b | Lösning c | Lösning 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}\,.

Svar | Lösning


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)

Svar | Lösning a | Lösning b | Lösning 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

Svar | Lösning a | Lösning b | Lösning 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}

Svar | Lösning a | Lösning b | Lösning 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}

Svar | Lösning a | Lösning b | Lösning c

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