## Question

###### The value of a car can be modelled by the function;300V = 18sin0<1<257coswhere, Vis the value f the car in thousands tis the time in years since the car was purchased.Express I8sin 0 + 7cos0 in the form R(sin0+a) where R > 0 and 0 < & Give the exact value of R and the value of & in radians, to 2 decimal places_Find the time, in years, that it will take for the car to be worth half of its original purchase price_Find the time taken for the value of the car to reach its minimum

The value of a car can be modelled by the function; 300 V = 18sin 0<1<25 7cos where, Vis the value f the car in thousands tis the time in years since the car was purchased. Express I8sin 0 + 7cos0 in the form R(sin0+a) where R > 0 and 0 < & Give the exact value of R and the value of & in radians, to 2 decimal places_ Find the time, in years, that it will take for the car to be worth half of its original purchase price_ Find the time taken for the value of the car to reach its minimum value. Explain with a reason why this model is not valid for large values of t. (Total for Question 7 is 10 marks)

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