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Question

5cosθ+3cos(θ+π3)+3

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Solution

5cosθ+3cos(θ+π3)+3

=5cosθ+3(cosθcosπ3sinθsinπ3)+3

=5cosθ+3cosθ123sinθ32+3

=132cosθ332sinθ+3

The range of acosθ+bsinθ+c is

c±(a2+b2)

Hence, the range of given function is

3± (132)2+(332)2

=4 & 10

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