Explanation y = θ + sin θ + cos θ Critical Points of θ + sin ( θ ) + cos ( θ ) : θ = π 2 + 2 π n , θ = π + 2 π n f ' ( θ ) = 1 + cos ( θ ) − sin ( θ ) d d θ ( θ + sin ( θ ) + cos ( θ ) ) Apply the Sum/Difference Rule : ( f ± g ) ' = f ' ± g ' = d d θ ( θ ) + d d θ ( sin ( θ ) ) + d d θ ( cos ( θ ) ) d d θ ( θ ) = 1 d d θ ( sin ( θ ) ) = cos ( θ ) d d θ ( sin ( θ ) ) Apply the common derivative : d d θ ( sin ( θ ) ) = cos ( θ ) = cos ( θ ) d d θ ( cos ( θ ) ) = − sin ( θ ) = 1 + cos ( θ ) − sin ( θ ) Solve 1 + cos ( θ ) − sin ( θ ) = 0 : θ = π + 2 π n , θ = π 2 + 2 π n 1 + cos ( θ ) − sin ( θ ) =

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Chapter 4.3, Problem 45E

To determine

y=θ+sinθ+cosθ

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Chapter 4.3, Problem 44E

Chapter 4.3, Problem 46E

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y = θ + sin θ + cos θ

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y=θ+sinθ+cosθ

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