Solving Trig Equations Multiple solutions for sin and cos Solving simple trig equations of form: sin k = c sin ak =c

Starter Put cards into 3 groups: = -1 = 0 = 1

Solving Trig Equations Multiple solutions for sin and cos Solving simple trig equations of form: sin k = c sin ak =c

Sine and Cosine By sketching a graph show that: sin  = sin(180 –  ) cos  = cos(360 –  ) Mini whiteboards

Use your graphs to find which of these are the same as cos Time allowed – 2 minutes Cos Cos Cos Cos Cos Cos Cos Cos -30 0

GDC Link to Casio emulator Use graph mode on GDC Remember to use y = & trig Use degrees or radians as appropriate Change y axis values for stretches

1.Solve the equations (a) and (b) for 2. Solve the equation for 3.Solve the equations ( giving answers correct to the nearest whole degree ) (a) for (b) for

1 Exercises The 2 nd solution is 1.Solve the equations (a) and (b) for Solution: (a) ( from calculator )

1 Solution: ( from calculator ) The 2 nd solution is (b) Exercises

2. Solve the equation for Exercise Solution: Principal value Ans: Adding

3.Solve the equations ( giving answers correct to the nearest whole degree ) (b) for (a) for Exercises

1 (a) for Solution: Principal value By symmetry, Ans: Exercises

1 1 Ans: (b) for Solution: Principal value Either:Or: Exercises

aims: To extend solving trig equations to: Sin ax Cos (ax+b) atan (bx+c) Including use of GDC

e.g.1 Solve the equation for the interval 1 st solution: Sketch to find the 2 nd solution: Solution: Let so, ( Once we have 2 adjacent solutions we can add or subtract to get the others. ) There will be 4 solutions ( 2 for each cycle ). We can already solve this equation BUT the interval for x is not the same as for.

So, For, the other solutions are So, N.B. We must get all the solutions for x before we find. Alternate solutions for are NOT apart. for

Activity 2 Tarsia puzzle: hexagon small groups Time allowed – 20 mins or

Mini whiteboards Solving simple trig equations quiz

Multiple solutions for sin and cos Solving simple trig equations of form: sin k = c asin bk =c sin ( x-30 o ) = c

e.g. (a) for Use and We can use the same method for any function of. e.g. (b) for Use and e.g. (c) for

Have a go! Adjust the interval where you’re finding the angles A5 worksheet

Tan 2θ What is the period of this graph?

Solving harder equations Principle value: Using periodicity: Solvewhen

Solving harder equations Principle value: Using periodicity: SolveWhen Using symmetry:

Solving harder equations Principle value: Using periodicity: Solvewhen Using symmetry:

Mini whiteboards Solving simple trig equations quiz

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