Beyond 0 360 Looking at the periodicity of

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

Sin Function ¢ When does sin x = 0 ? On your calculator… Is this the only value of x? Inv sin (0) = 00 On a calculator try: Sin 1800 = 0 Sin 3600 = 0 Sin 5400 = 0 Sin 7200 = 0 How can they all be right?

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

The Sin Function ¢ Us the graph to help you find the first values of x for which sin x = 1 90 450 What will be the next value? What is the pattern? + 360 810

The sin function ¢ Find 4 value of x for which sin x = 0. 2 120 3720 1680 5280 Use symmetry to find x = 1680 On your calculator… Inv sin (0. 2) = 120 Use the fact that the function repeat after 3600 to find: x = 372 x = 528

The Sin Function ¢ Find five value of x for which sin x = 0. 5 300 1500 3900 5100 On your calculator… Inv sin (0. 5) = 300 Hint: Use the fact that each part of the curve is symmetrical

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

The Cosine Function ¢ Find four values of x for which cos x = 0. 75 410 3190 On your calculator… Inv cos (0. 75) = 410 4010 6790