TVOILC MHF4U Learning Activity 3.12 Unit 3 Assignment Solve the equation between 0 and 2, 3sin?(x) + sin(x) = 1 3 sin?(x) [6 mark] Solve the inequality to two decimal places where 0 m [4 marks] The number of hours of sunlight in a day of a leap year, in part of Ontario, can be modelled by a sinusoidal function with a minimum of 8.9 on the 356" day of the year (December 21%), and a maximum of 15.4 on the 173 day of the year (June 21%!). a. Find a sinusoidal function that models this relationship. [5 marks] b. What days (on the calendar) are the closest to 14 hours in length? [4 marks] c. How long is the 218" day of a leap year? [1 mark] For each equation, either prove that it is an identity or give a counterexample that proves it is not. Describe the process you followed. [12 marks] a. tan(a + b) = tan(a) + tan (b) b. tan(x + m) = tan(x) c. cos(2x) = sin*(x) cos*(x) sin(x) cos(x)sin(x) d. cot(x) csc(x) = e Given the expression 2 cot(x) 2 cot(x) cos?(x), a. Use technology to graph the expression [3 marks] b. Determine an equivalent trigonometric expression [2 marks] c. Then prove that your expression is equal to the given expression. [3 marks] Explain the difference between a periodic function and a sinusoidal function. Include an image or values as an example in your response. [4 marks] Describe two examples of real-life data that could be periodic. For each, explain what you would expect the period to be, and a practical method you could use to measure data and create a model. [6 marks]