5) (4 marks) Determine a possible equation for the following sinusoidal function. 0 I'll? rt 311-2 211 _ :25 ._ 6) (2 marks) Express sin[ + 6'] as a single trigonometric function in simplest form. 2 7) (1 mark) Determine the exact value of cos[ + E] 8) (10 marks) Determine the exact measure(s) of the angle 6, whereO s 9 S 272*. a. IOsec6+2 = 18 b. sin29+cos6=0 Application 9) (9 marks) The height of a nail in a bicycle tire as it rotates around is periodic in nature. The radius of the tire is 200m and at the current pedalling speed the tire rotates once every second. a. Determine the equation of a sinusoidal function that models this situation assuming that the nail starts on the ground at time zero. b. At what time(s) during the rst two seconds is the nail at a height of 10cm? 10) (3 marks) A swimmer on a oating air mattress will follow the rise and fall of the waves in lake. When the person is on the top of the wave her feet are 0.5m above the average surface height of the lake. When she is in a trough her feet dig 0.5m into the water (-0.5m). The peaks of the waves are separated by two seconds. Create an equation of the sinusoidal inction that models this movement assuming that she starts at the average surface height of the lake and heads upwards