# Form 4 Mathematics graphs of trigonometric functions questions and answers

Form 4 Mathematics graphs of trigonometric functions questions and answers

Lessons (**19**) * SHARE*

- 1.
Complete the table given below by filling in the blank boxes.
Taking 1cm to represent #15^0# on the x-axis and 2cm to represent 1 unit on the y axis, draw the graph of
y=3cosx and y=4sin(2x-#10^0#) using the same axes on the graph paper provided. Use your graph to find the value of x for which 3 cosx=4sin(2x-#10^0#)

17m 53s - 2.
(a) Complete the table given below by filling in the blank boxes.
(b) On the same axes draw the graph of y= 3 sin #x^0#-1 and y=#cosx^0# on the grid below.
(c) Use your graph to solve the equation, #3sinx^0#- #cosx^0#=1

16m 0s - 3.
Complete the table below by filling in the blank spaces.
Draw the graph of y=2 sin x and y= cos 2x using the axes on the grid provided.
(a) What is the difference in the values of y=2 sin x and y= cos 2x at x=#(67 1/2 )^0#?
(b) State the periods of
(i) y=2 sinx
(ii) y=cos 2x

19m 55s - 4.
(a) Complete the table below for the function y= 2 sin 3x #0^0 le x le 120^0#.
(b) (i) Using the values in the completed table, draw the graph of y= 2sin 3x for on the provided
(ii) Hence solve the equation 2 sin 3x= -1.5

17m 57s - 5.
Complete the table given below for the functions y=-3 cos#2^0# and y=2sin(#2/3 x^0+30#) for #0^0lexle180^0#
(a) Using the grid provided, draw the graph of y=- 3 cos #2^0# and y=2 sin(#2/3 x^0+30#) on the same axis. Take 1 cm to represent #20^0# on the xaxis and 2 cm to represent one unit on the y- axis.
(b) From the graph, find the roots of 3 cos #2^0#+2 sin(#2/3 x^0+30#)

15m 46s - 6.
Complete the table below by filling in the blank spaces.
Using the scale 1 cm to represent #30^0# on the horizontal axis and 4 cm to represent 1 unit on the vertical axis, on the grid provided, draw the graph of y=cos#x^0# and y=2cos#1/2 x^0# on the same axis.
(a) Find the period and the amplitude of y=2 cos #1/2 x^0#
(b) Describe the transformation that maps the graph of y= cos #x^0# on the graph

16m 16s - 7.
(a) Complete the table below for the values of y=2 sin x+cos x.
(b) Using the grid provided, draw the graph of y=2 sin x+cos x for #0lexle360^0# Take 1 cm to represent #30^0# on the x axis and 2 cm to represent one unit on the y- axis.
(c) Using the graph to find the range of values of x that satisfy the inequality 2 sin x+cos X#gt# 0.5

12m 0s - 8.
(a) Complete the table below, giving your values correct to 2 decimal places.
(b) On the grid provided, draw the graphs of y= tan x and y= sin (#2x+30^0#) for #0^0lexle70^0# Take the scale: 2 cm for #10^0# on the x axis 4 cm for 1 unit on the y axis
(c) Use the graph to solve the equation: tan x-= sin(2x+#30^0#)=0

12m 55s - 9.
(a) Complete the table for the equation y= 2sin #(3x+30^0)#
(b) Using the grid provided, draw the graph of 2sin#(3x+30^0)# for #0^0lexle90^0# Take 1 cm tob represent #5^0# on the xaxis and 2 cm to represent 1 unit on the y-axis.
(c) Use the graph in (b) to find the range of values that satisfy the inequality #yge1.6#

9m 34s - 10.
(a) Complete the table given below by filling in the blank spaces.
(b) On the grid provided draw, on the same axes, the graph of y=3 cos 2x and y = 2sin#(2x+30^0)# for #0^0lexle180^0# Take the scale 1 cm for #15^0# on the x-axis and 2 cm for 1 unit on the y-axis,
(c) Use the graph to estimate the range of values of x for which 3cos#2xlesin(2x+30^0)# Give your answer to the nearest degree.

15m 19s - 11.
(a) Complete the table below giving your values to correct 2 decimal places.
(b) Using the grid provided and the table in part (a) draw the graph of y= tan#theta# and y=sin2#theta#
(c) Using your graphs, determine the range of values for which tan #thetagesin2theta # for #0^0lexle90^0#

13m 9s - 12.
(a) Complete the table below, giving your values correct to 2 decimal places.
(b) Using the grid provided, draw the graph of y= cos 2 x and y=sin(x+#30^0#) for #0^0lexle180^0# Take 1 cm to represent #15^0# 0 on the x-axis and 4 cm to represent 1 unit on the y-axis.
(c) Find the period of the curve y=cos2x
(d) Using the graph in part
(b) above, estimate the solutions to the equation sin #(x+30^0)#

11m 57s - 13.
(a) Complete the table below giving your values to correct 2 decimal places.
(b) On the grid provided, using the same scale and axes draw the graph of y=2sin#x^0# and y=1-cos#x^0# for #0^0lexle180^0# Take the scale: 2 cm for
#30^0# on the x-axis 2 cm for 1 unit on the y-axis.
(c) Use the graph in (b) above to
(i) Solve the equation #2sinx^0+cosx^0=1#
(ii) Determine the range of the values of x for

11m 35s - 14.
(a) Given that y= 8 sin 2xcos 6x, complete the table below for the missing values of, correct to 1 decimal place.
(b) On the grid provided below, draw the graph of y= 8 sin 2x – cos 6x for #0^0lexle120^0# Take the scale: 2cm for #15^0# on the x-axis and 2cm for 2 units on the y-axis
(c) Use the graph to estimate:
(i) The maximum value of y
(ii) The value of x for which 4 sin 2x- 3cos x=1

11m 25s - 15.
(a) Complete the table below, giving your values correct to 2 decimal places.
(b) On the grid provided draw the graphs of y= sin 2x and y=3 cos x-2 for #0^0lexle360^0# on the same axes. Use a scale of 1 cm to represent #30^0# on the x-axis and 2 cm to represent 1 unit on the y-axis
(c) Use the graph in (b) above to solve the equation 3 cos x- sin 2x=2.
(d) State the amplitude of y= 3 cos x-2

15m 49s - 16.
(a) Complete the table below, giving your values correct to 2 decimal places.
(b) On the grid provided, using the same scale and axes draw the graph of y=cos #x^0# and y=sin #x^0# - cos #x^0# for #0^0lexle180^0# Using the scale: 1
cm for #20^0# on the x-axis 4 cm for 1 unit on the y-axis.
(c) Using the graph in part
(b)
(i) Solve the equation #sinx^0-cosx^0=1.2#
(ii) Solve the equation

14m 56s - 17.
The table below shows values of x and y for the function y=2 sin 3#x^0# in the range
#0^0lexle150^0#
(a) On the grid provided draw the graph of y=2 sin 3#x^0#
(b) From the graph determine the period

6m 47s - 18.
(a) Complete the table below giving your values to correct 1 decimal place.
(b) On the grid provided, using the same scale and axes draw the graph of
y=2sin(#x+20^0#) and y=#sqrt3# cos x for #0^0lexle240^0#
(c) Using the same graphs drawn in (b) above to
determine:
(i)the values of x for which 2sin(#x+20^0#)=#sqrt3# cosx
(ii)the difference in the amplitude of y=2sin(#x+20^0#) and y=#sqrt3# cos

15m 5s - 19.
The equation of the curve is given by y= 1+3 sin x.
(a) Complete the table below for y= 1+3 sin x.
(b)(i) On the grid provided, draw the graph of y= 2sin #x^0# and y= 1+3 sin x. For #0^0lexle360^0#
(ii) state the amplitude of the curve.
(c)On the same grid draw the graphs of y= tan x for #90^0lexle270^0#
(d)Use the graphs to solve the equation 1+3 sin x=tan x for

14m 42s

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