1. MATHPOWER TM 12, WESTERN EDITION 5.3 5.3.1 Chapter 5 Trigonometric Equations

2. Interpreting Graphs to Find Solutions The diagram below shows the graphs of two trig functions, y = 4sin 2 x and y = 6sinx + 2, defined for 0 ≤ x ≤ 2  Describe how you could use this graph to estimate the solution to the equation (4sin 2 x)(6sinx + 2) = 0 for 0 ≤ x ≤ 2  y= 4sin 2 x y = 6sinx + 2 5.3.2

3. Interpreting Graphs to Find Solutions Describe how you could use this graph to estimate the solution to the equation 4sin 2 x = 6sinx + 2 for 0 ≤ x ≤ 2  y= 4sin 2 x y = 6sinx + 2 5.3.3

4. 4sin 2 x - 6sinx - 2 = 0 5.3.4 Interpreting Graphs to Find Solutions An alternative to solving the equation 4sin 2 x = 6sinx + 2 for 0 ≤ x ≤ 2  is to rewrite the equation with the right hand side equal to zero, then the solutions would be the x-intercepts. Therefore, the solutions are:

5. Interpreting Graphs to Find Solutions Use a graph to solve the equation Therefore, the solutions are: 5.3.5

6. Using Technology to Find Solutions 5.3.6 Determine the lowest possible value of x, to the nearest tenth, for which The smallest x-value is

7. Using Technology to Find Solutions 5.3.7 An alternate method is to graph The smallest x-value is

8. 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