mathematics
  Personalized »

KS3
 
 
 
Year 7
 
 
Year 8
 
 
Year 9

KS4
 
 
 
Year 10
 
 
Year 11

A-levels
 
 
 
Year 12 (AS)
 
 
Year 13 (A-levels)


physics
  Personalized »

 
 


KS4
 
 
 
KS4 Level Physics

A-levels
 
 
 
AS Level Physics
 
 
A-levels Physics


 
 
Private tutors
 
 
Find a tutor »


 


Unlock access to content
 
Select one option:



Free of charge
Unlock the chapter   "Trigonometric Graphs"  



Unlock access to the solution of problems in this chapter.
Free of charge Price: 3.00 £

Continue »
Subscribe to OpenProf     If you do not get a better grade, you get your money back!
 


Unlock access to all problems solutions.
Available from 8.25 £ / month.
Continue »
mathematics UK Year 12 Mathematics (AS)
 
Solved problems for the chapter:
 

Trigonometric Graphs

download pdf
View the theory »
Graph of sine and cosine functions
open
↓   Show theory [1]   ↓


Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:trigonometric_graphs/4714/


Example 1.
Draw the graph of the function and write down the range of values:

    
Example 2.
Draw the graph of the function and write down the range of values:

    
3.
Draw the graph of the function and write down the range of values:

    
4.
Draw the graph of the function and write down the range of values:

    
5.
Draw the graph of the function and write down the range of values:

    
6.
Draw the graph of the function and write down the range of values:

    
7.
Draw the graph of the function and write down the range of values:

    
8.
Write down the basic period and amplitude of the function:

    

9.
Write down the basic period and amplitude of the function:

    
10.
Solve the equation:

    
11.
Solve the equation:

    
12.
Draw the following graphs in the same coordinate system:

    
13.
Write down the basic period and amplitude of the function:

    
14.

Given the graph of the function , first move it parallel by in the direction of the x-axis, reflect over the x-axis, then stretch it by a factor of - 2 in the direction of the y-axis and then move it in parallel by 1 in the direction y-axis.


  • Obtain the equation of the obtained function.


  • Obtain the domain and range of the function.


  • Calculate the zeros of the function.

    
15.

Draw the graphs of the following in the same coordinate system:


    
16.
Draw the following graphs in the same coordinate system:

    
17.

Draw the graphs of the following in the same coordinate system:


    
18.
Draw the graph of the function:

    

19.

In the same coordinate system, plot the graph of the functions f and g.




where






Write down their intersections.

    
20.
Draw the graph of the function:

    
21.

The function is given.


  • Draw the graph of the function on the interval .


  • Obtain the zeros of the function and its range of values.


  • At what interval is the function decreasing?

    
22.

The function is given.


  • Obtain the zeros of the function.


  • Draw the graph of the function f and write down its range of values.


  • Obtain the abscissas of the maxima and minima of the function.


  • Draw the graph of the function in the same coordinate system

    
23.

In the same coordinate system draw the graph of functions .




and




and write down their intersections.

    
24.

Draw the graph of the functions below in the same coordinate system:




and




and write down their intersections.

    
25.
Draw the following graphs in the same coordinate system:

    
26.
Write down the zeros and abscissas of the maxima and minima of a given function.

    
27.
Write down the zeros and abscissas of the maxima and minima of a given function.

    
28.
Write down the zeros and abscissas of the maxima and minima of a given function.

    

29.
Write down the zeros and abscissas of the maxima and minima of a given function.

    
30.
Solve the equation:

    
31.
Draw the graph of the function below and obtain the range of values:

    
32.
Draw the graph of:

    
33.
Solve the equation:

    
34.
Solve the equation:

    
35.
Solve the equation:

    
36.
Solve the equation:

    
37.
Solve the equation:

    
38.
Draw the graph of:

    

39.
Draw the graph of the function below and obtain the range of values:

    
40.
Draw the graph of the function below and obtain the range of values: