Which of the following functions have a vertical asymptote for values of θ such that cos θ = 1? Select two answers. a.) y = sin θ b.) y = cos θ c.) y = tan θ d.) y = sec θ e.) y = csc θ f.) y = cot θ

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Well costheta=1, at 0, 2pi,...  knowing this we can exclude the first two as the are not undefined anywhere.  tan is sin/cos, at 0 sin is also 0 so it becomes 0/1 which is 0, not undefined. sec is1/cos, cos is 1, this is just 1 csc is 1/sin, sin is 0, 1/0 is undefined, meaning there will be an asymptote  cot is cos/sin, this is again 1/0, so it is also an asymptote The last two answers are the ones you want

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