Periodic functions > The cosine function
123456The cosine function

Exercises

Exercise 1

Given is the graph of f ( x ) = cos ( x ) .
Solve the following equations. Give exact answers where possible, approximations in three decimals otherwise.

a

cos ( x ) = 0,35

b

cos ( x ) = -0,35

c

cos ( x ) = 1 2 3

d

cos ( x ) = - 1 2 2

Exercise 2

Give all solutions of:

a

cos ( x ) = 1

b

cos ( x ) = cos ( 1 )

c

cos ( 1 ) = x

d

cos ( x ) = sin ( 1 )

Exercise 3

Given the function f with f ( x ) = 2 cos ( x ) - 1 on [ 0 , 4 π ] .

a

Compute all zeroes of the graph of this function.

b

Solve: f ( x ) 0 .

Exercise 4

Given the function g with g ( x ) = cos ( 2 x ) on [ 0 , 4 π ] .

a

Solve: g ( x ) = 0 , 5

b

Solve: g ( x ) 0,5 .

Exercise 5

Compute the exact solutions on [ 0 , 2 π ] .

a

sin ( x ) ( 2 cos ( x ) - 1 ) = 0

b

sin 2 ( x ) = sin ( x )

c

cos 2 ( x ) - 1 , 5 cos ( x ) - 1 = 0

d

2 sin 2 ( x ) + cos ( x ) = 0

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