Question

Sketch y = 2 sin(x) + x - 2 (b) This graph intersects the x-axis exactly...

Sketch y = 2 sin(x) + x - 2

(b) This graph intersects the x-axis exactly once.

(i) Show that the x-intercept of the graph does not lie in the interval (0, 0.7)

(ii) Find the the value of a, 0<a<1 for which the graph will cross the x-axis in the interval (a, a + 0.1) and state this interval

(iii) Given x = alpha is the root of the equations 2 Sin(x) + x - 2 = 0, explain why alpha lies in the interval (a, a + 0.1)

(iv) The equation 2 Sin(x) + x - 2 = 0 can be solved by obtaining the point of intersection of two graphs, one of which is y = sin(x)

(a) What is the equation of the other graph??

(b) Express the coordinates of the point of the intersection of the two graphs as algebraic expression in terms of alpha.

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This is graph.

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