Let `f : [ 0, (pi)/(2)] → R, \ f(x) = 4 cos(x)` and `g : [0, (pi)/(2)] → R, \ g(x) = 3 sin(x)`.
- Sketch the graph of `f` and the graph of `g` on the axes provided below. (2 marks)
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- Let `c` be such that `f(c) = g(c)`, where `c∈[0, (pi)/(2)]`
Find the value of `sin(c)` and the value of `cos(c)`. (3 marks) - Let `A` be the region enclosed by the horizontal axis, the graph of `f` and the graph of `g`.
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- Shade the region `A` on the axes provided in part a. and also label the position of `c` on the horizontal axis. (1 mark)
- Calculate the area of the region `A`. (3 marks)