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Using Trig Identities to Solve a Quadratic in Sin x
The mathematical solution explains how to use the identity sin2x + cos2x≡ 1 to form a quadratic equation which can then be solved in a given range. The method of 'splitting the middle term' is used in order to help factorise the resulting quadratic in sin2x. The two resulting equations are then considered separately in order to obtain all the solutions within the required range. The solution is then verified by considering the appropriate graph.
The graphical solution explains how to use the graphic calculator to draw the two graphs featuring in the original equation and exploring their points of intersection in order to verify the solution found using the mathematical solution.
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