TRIGONOMETRIC EQUATIONS Solving Inequalities (Page 5 of 6)

The solutions to the equation (within the given interval) are x = 70.6 and x = 313.9, approximately. We now interpret the inequality sin[(2pi/365)(x-121)]+(1/2) < 0 in terms of the function we have graphed. The solution set will be all values of x for which the function Y1 has negative y-values. Let's use TRACE to identify where these values of x are.

 TRACE key. Left arrow key....

 Right arrow key....

 Calculator screen image. Calculator screen image. Calculator screen image.

Since the x-intercepts have a y-value of 0, they are not part of the solution set. The x-values to the left of 70.6 yield negative y-values, as well as the x-values to the right of 313.9.
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