MATHPOWERTM 12, WESTERN EDITION

1
Chapter 5 Trigonometric Equations
5.3
Using Technology to Solve More Complex Equations
5.3.1
MATHPOWERTM 12, WESTERN EDITION
2
Interpreting Graphs to Find Solutions
The diagram below shows the graphs of two trig
functions, y 4sin2x and y 6sinx 2, defined
for 0 x 2p.
Describe how you could use this graph to estimate
the solution to the equation (4sin2x)(6sinx 2)
0 for 0 x 2p.
y 6sinx 2
y 4sin2x
The solutions will be the points where the graphs
intersect the x-axis. Therefore, the solutions
are
x 0, 3.14, 6.28, 3.48, and 5.94
5.3.2
3
Interpreting Graphs to Find Solutions
Describe how you could use this graph to estimate
the solution to the equation 4sin2x 6sinx 2
for 0 x 2p.
y 6sinx 2
y 4sin2x
The solutions will be the points where the graphs
intersect. Therefore, the solutions are
x 3.426 and 5.999
5.3.3
4
Interpreting Graphs to Find Solutions
An alternative to solving the equation 4sin2x
6sinx 2 for 0 x 2pis to rewrite the
equation with the right hand side equal to zero,
then the solutions would be the x-intercepts.
4sin2x - 6sinx - 2 0
Therefore, the solutions are x 3.426 and 5.999
5.3.4
5
Interpreting Graphs to Find Solutions
Use a graph to solve the equation
Therefore, the solutions are x 0 and 2.2789
5.3.5
6
Using Technology to Find Solutions
Determine the lowest possible value of x, to the
nearest tenth, for which
The smallest x-value is -2.9.
5.3.6
7
Using Technology to Find Solutions
An alternate method is to graph
The smallest x-value is -2.9.
5.3.7
8
Assignment
Suggested Questions Pages 252 and 253 17, 25,
31, 34 b, 35 a Pages 256 and 257 1, 4, 5, 8 abc
5.3.8