1 Pure Mathematics
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Question 850
Figure 1 below shows the graph of y=cosxy = \cos xy=cosx, where x x\,x is measured in radians.
a.[2]
Explain why the equation cosx−3x−0.5=0\cos x - 3x - 0.5 = 0cosx−3x−0.5=0 has only one real root.
b.[3]
Given that the root of the equation is α\alphaα, and that α \alpha\,α is small, use small angle approximations to find the value of α \alpha\,α to three decimal places.