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Finding All the Solutions of Trigonometric Equations

The mathematical solution explains how to solve the equation: sin(x+150) = 1/sqrt2 for x between 0⁰ and 360⁰. To begin with, the principle values for (x+150) are found. The fact that a sine curve is periodic is used to find the solution set for (x+150) based upon these two initial values. Subtracting 150 from each member of the solution set gives a solution set for x. From this solution set values for x in the required range can be identified.

Graphical solution 1 shows how a graphical calculator can be used to verify the solution. The first step is to use the calculator to draw the graph of y=sin(x+150) and the graph of y= 1/sqrt2. The graphical calculator is then used to find the points of intersection of the two graphs confirming the mathematical solutions.

Graphical solution 2 shows the mathematical solution to the equation cos(4x) = -1/2 and explains how the solutions found can be verified graphically by finding the points of intersection of the graphs y= cos(4x) and y= -1/2.


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