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Solving a Quadratic Equation in Sin(x)
The mathematical solution explains how to solve the equation: 6 cos2x +7sinx = 8 for x between 0 and 4π radians. The equation is rearranged to make the equation 6 cos2x +7sinx - 8 = 0 then the identity sin2 x + cos2x ≡1 used to form a quadratic equation in one variable. The quadratic formed can be factorised and solved finding the principle values in radians. The fact that a sine curve is periodic is used to find the solution set. From this solution set values for x in the required range can be identified.
Graphical calculator solution 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=6 cos2x +7 sin x and the graph of y= 8. The graphical calculator is then used to find the points of intersection of the two graphs confirming the mathematical solutions. The video emphasises the need for the calculator to be in radians mode and the need to choose an appropriate scale on the calculator in order to show the points of intersection clearly.
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