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A2 trig eg no.5
In the first part, we need to find out the values of 'R' and 'α'. We are given the equation 'cos θ + (√3) sin θ' and using this we can easily calculate the values of 'R' and 'a'. To find 'R', we'll use the formula √[(a)^2 + (b)^2] and to find 'α', we'll use the formula tan α = (b)/(a). Doing it step by step, here's how it's done:
Finding 'R':
R=√[(a)^2 + (b)^2]
R=√[(√3)^2 + (1)^2]
R=√[3+1]
R=√4
R=2
Finding 'α':
tan α = (b)/(a)
tan α = (√3)/(1)
α = tan^-1 (√3)
α = 1.05 rad.
We can now insert the values of 'R' and 'α' in the given equation 'R cos(θ − α)' so that it becomes '2 cos (θ - 1.05)'.
Now the second part of the question consists of integration. The attached file will tell you how it's done: