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Given the graphs of f(x) = k sin x and g(x) = cos(x + n), determine the values of k and n.

Mathematics

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Here's a step-by-step solution for each part of Question 1.2:

Part 1.2.1: Write down the value of kk and nn.
The graphs are f(x)=ksin⁡xf(x) = k \sin x (green curve) and g(x)=cos⁡(x+n)g(x) = \cos(x + n) (pink curve).

  • For f(x)=ksin⁡xf(x) = k \sin x: From the graph, the maximum value of f(x)f(x) is 2 at x=90∘x = 90^\circ. Substituting this into the function: f(90∘)=ksin⁡(90∘)=k(1)=kf(90^\circ) = k \sin(90^\circ) = k(1) = k
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