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33: The equation 33: The equation © Christine Crisp “Teach A Level Maths” Vol. 2: A2 Core Modules

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The equation "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" Module C3 Edexcel Module C4 AQA MEI/OCROCR

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The equation Can you see why one of these equations is easy to solve and the other takes much more work ? (a) (b) Both have 2 trig ratios but (a) can be solved by dividing by. We get This is a simple equation and can now be solved.

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The equation If we try the same method with (b), we get This is no better than the original equation as we still have 2 trig ratios. Can you see why one of these equations is easy to solve and the other takes much more work ? (a) (b)

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The equation However, we saw in the previous section that so the equation can be written as Dividing by 5: This is of the form where so we can find solutions for and then find x by adding to each one.

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The equation e.g. 1 Solve the following equation giving the solutions in the interval correct to 1 d.p. Solution: Let Coef. of :

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The equation Substituting into the l.h.s. of the equation: At this stage we need to get all the solutions for. So, Beware ! Don’t find x at this stage. We have NOT The 2 nd solution will be wrong if we use the x value to try to find it. ( Subtract from each part )

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The equation We sketch the usual cosine graph: Outside the required interval

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The equation We sketch the usual cosine graph: Add : ANS: x is ( 1 d.p. )

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The equation SUMMARY To solve the equation Write the l.h.s. in one of the forms Solve the equation to find making sure you find all the solutions. Calculate the interval for using the one given for x, where or. Find the values of x. N.B. for, add and for, subtract .

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The equation Exercise 1(a) Write in the form where R and are exact. (b) Solve the equation 2. Solve the equation for for. ( Notice the different letter in the equation. You need to be able to cope with a switch of letters. )

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The equation 1(a) Solutions: Coef. of : So,

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The equation Solutions: so, the equation becomes for.1(b)Solve

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The equation Solutions: Coef. of : So, 2. SolveLetSo,becomes

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The equation Solutions: for.Solve

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The equation

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The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied. For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

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The equation (a) (b) Both have 2 trig ratios but (a) can be solved by dividing by. We get This is a simple equation and can now be solved. Think about these 2 equations.

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The equation If we try the same method with (b), we get This is no better than the original equation as we still have 2 trig ratios. so the equation can be written as Dividing by 5: However, we saw in the previous section that This is now a simple equation which can be solved.

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The equation e.g. 1 Solve the following equation giving the solutions in the interval correct to 1 d.p. Solution: Let Coef. of :

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The equation Substituting into the l.h.s. of the equation: At this stage we need to get all the solutions for. So, Beware ! Don’t find x at this stage. We have NOT The 2 nd solution will be wrong if we use the x value to try to find it. ( Subtract from each part )

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The equation We sketch the usual cosine graph: Add : ANS: x is ( 1 d.p. )

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