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4.4 Exercises

From Förberedande kurs i matematik 1

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       Theory          Exercises      

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

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f | Solution 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

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Exercise 4.4:3

Solve the equation

a) cosx=cos6 b) sinx=sin5
c) sin(x+40)=sin65 d) sin3x=sin15

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 4.4:4

Determine the angles v in the interval 0v360 which satisfy  cos2v+10=cos110 .

Answer | Solution


Exercise 4.4:5

Solve the equation

a) sin3x=sinx b) tanx=tan4x
c) cos5x=cos(x+5)

Answer | Solution a | Solution b | Solution c

Exercise 4.4:6

Solve the equation

a) sinxcos3x=2sinx b) 2sinxcosx=cosx 
c) sin2x=−sinx

Answer | Solution a | Solution b | Solution c

Exercise 4.4:7

Solve the equation

a) 2sin2x+sinx=1 b) 2sin2x−3cosx=0
c) cos3x=sin4x

Answer | Solution a | Solution b | Solution c

Exercise 4.4:8

Solve the equation

a) sin2x=2cosx  b) \displaystyle \sin{x}=\sqrt{3}\cos{x}
c) \displaystyle \displaystyle \frac{1}{\cos^2{x}}=1-\tan{x}

Answer | Solution a | Solution b | Solution c

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