Homework Pg. 376 # 15, 16, 17, 19, 20 Pg. 388 # 12(a,b,c), Having trouble? Come to room 120 any day at lunch for help! Videos Links Powerpoint from class

Focus Time No talking No eye-contact

Common mistakes... 1.The 2 in the following equation causes a horizontal compression, not expansion y = sin2(x) 2. The horizontal shift for the following equation is 2π, not 4π. The k value must be on the outside of the brackets, if it’s on the inside you need to factor it out. y = cos(2x + 4π) y = cos2(x + 2π)

Common mistakes The following equation represents a horizontal shift of π to the LEFT y = sin(x + π) but it would be shifted RIGHT if it was y = sin( x – π) 4.Transformations CANNOT be done in random order, the correct order is: 1.Stretches & Compressions 2.Reflections 3.Translations

The pendulum in a grandfather clock can be modelled by the equation D(t) = 0.5sinπ(t + 0.5) Where D is the distance from the middle and t is the time in seconds. How long does it take this clock to swing through one cycle? If you released the pendulum from the right as shown above at time t = 0, where is the pendulum 1.5 seconds later? Do this using the equation, then graph it to check.

New period = 2π2π k Period can be in terms of angles (radians & degrees) or in terms of time But the equation you use is still the same!

Homework Pg. 376 # 15, 16, 17, 19, 20 Pg. 388 # 12(a,b,c), Having trouble? Come to room 120 any day at lunch for help! Videos Links Powerpoint from class

Focus Time No talking No eye-contact

A ferris wheel has a diameter of 32 m, its centre is 18m above the ground and takes 30s to complete a revolution. a) Graph a rider’s height above the ground, in metres, versus the time, in seconds, during a 2-min ride. The rider begins at the lowest position on the wheel

A ferris wheel has a diameter of 32 m, its centre is 18m above the ground and takes 30s to complete a revolution. b) Determine the equation of this graph as if it were a SINE graph

a = 16

k = π/15

d = c = + 18

A point on the ocean rises and falls as tsunami waves pass. Suppose that a wave passes every 15 mins, and the height of each wave from the crest to the trough is 10 metres. a)Sketch a graph to model the depth at the point relative to its average depth for a complete cycle, starting at the trough of the wave b)Determine the equation for your sketch in part a) as if it were a SINE graph

A point on the ocean rises and falls as tsunami waves pass. Suppose that a wave passes every 15 mins, and the height of each wave from the crest to the trough is 10 metres. c)Re-draw the graph to model the height of the point relative to the ocean floor (which is 15 metres below the trough) d)Determine the equation for your sketch in part c) as if it were a SINE graph

The water depth near Sendai Japan fluctuated between 35m and 40m the day after the earthquake. One cycle was completed approximately every 3 hours. a)Draw a graph of the function for 12 hours after high tide which occurred at midnight. b)Find an equation for the water depth as a function of the time (in hours) after high tide as if it were a SINE graph c)What is the depth of water at 3pm?

Test is moved one class later!

Photo Hunt

Math Hunt The next few slides show a graph and an equation that do not match. Either change the graph or change the equation so that they do.

y = 0.5cos3(t) – 2

y = 0.25cos3π(t) - 2

y = 4.5sin(t + 0.5π) + 13

y = 4.5sinπ(t + 0.5) + 13

y = 3sin(0.5x ) + 1

y = 3sin2(x – 0.125) + 1

y = 2.4cos6(t + 2)

y = 1.2cos(π/6)(t-2)

y = 28cos(2π/365)(t + 18) + 19

y = 14cos(2π/365)(t - 73) + 19