Find all the points on the graph of the function [tex]f(x) = 2 \sin x + \sin^2 x[/tex] at which the tangent is horizontal.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f'(x) = 2 \cos x + 2 \sin x \cos x = 0[/tex]

[tex]2 \cos x (1 + \sin x) = 0[/tex]

[tex]\cos x = 0[/tex] or [tex]\sin x = -1[/tex]

[tex]x = \frac{\pi}{2} + n\pi[/tex] or [tex]x = \frac{3\pi}{2} + 2n\pi[/tex]

I then plug in to find the y-coordinates. However, the book's answer for the cos x = 0 part is [tex]x = \frac{\pi}{2} + 2n\pi[/tex]. But cos x = 0 for all [tex]x = \frac{\pi}{2} + n\pi[/tex]... right??? where did the 2 come from????

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# Homework Help: Trigonometry in this calculus problem

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