1. Using Technology to Solve More Complex Equations 5.3
Chapter 5 Trigonometric Equations
5.3
Using Technology
to Solve More
Complex Equations
MATHPOWERTM 12, WESTERN EDITION
5.3.1

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 = 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 = 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
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