Final answer:
To solve the trigonometric equation sin(5x) cos(9x) −cos(5x) sin(9x) =−0.55, use the angle addition formula for sine and find the values of x for which sin(14x) is equal to -0.55. The correct solution is x=2/π.
Step-by-step explanation:
To solve the trigonometric equation sin(5x) cos(9x) −cos(5x) sin(9x) =−0.55, we can use the angle addition formula for sine: sin(a+b) = sin(a)cos(b)+cos(a)sin(b). Let's rewrite the equation using this formula:
sin(5x+9x) = -0.55
sin(14x) = -0.55
Next, we can find the values of x for which sin(14x) is equal to -0.55. We can use either a graphing calculator or tables of values to find the approximate solutions.
Based on the options given, x= 2/π (Option A) is the correct solution to the equation.