1. Beyond 360 0 Looking at the periodicity of the sin and cosine functions

2. Sin Function When does sin x = 0 ? On your calculator… Inv sin (0) = 0 0 Is this the only value of x? On a calculator try: Sin 180 0 Sin 360 0 Sin 540 0 Sin 720 0 = 0 How can they all be right?

3. The Sin Function This is the sin function. Notice how it repeats itself… Sin x = 0 when x is0, 180, 360, 540, 720….. Can you predict the next value?What is the pattern?900 + 180

4. The Sin Function Us the graph to help you find the first values of x for which sin x = 1 90450 What will be the next value?810 What is the pattern? + 360

5. The sin function Find 4 value of x for which sin x = 0.2 On your calculator… Inv sin (0.2) = 12 0 12 0 372 0 Use symmetry to find x = 168 0 168 0 Use the fact that the function repeat after 360 0 to find: x = 372 x = 528 528 0

6. The Sin Function Find five value of x for which sin x = 0.5 On your calculator… Inv sin (0.5) = 30 0 30 0 150 0 390 0 510 0 Hint: Use the fact that each part of the curve is symmetrical

7. The Cosine Function Look at the cosine function. Can you see the repeating pattern? Cos x = 0 when…. x = 90, 270, 450, 810… Cos x = 1 when…. x = 0, 360, 720, …

8. The Cosine Function Find four values of x for which cos x = 0.75 On your calculator… Inv cos (0.75) = 41 0 41 0 319 0 401 0 679 0