solve the equation for all exact solutions where appropriate. round approximate answers in degrees to the…

solve the equation for all exact solutions where appropriate. round approximate answers in degrees to the nearest tenth. write answers using the least possible nonnegative angle measures. \n\ncscθ−1=0\n\nchoose the correct answer below.\n\n○a.{90°+180°n, where n is any integer}\n\n○b.{90°+360°n,270°+360°n, where n is any integer}\n\n○c.{90°+180°n,270°+180°n, where n is any integer}\n\n○d.{90°+360°n, where n is any integer}

solve the equation for all exact solutions where appropriate. round approximate answers in degrees to the nearest tenth. write answers using the least possible nonnegative angle measures. \n\ncscθ−1=0\n\nchoose the correct answer below.\n\n○a.{90°+180°n, where n is any integer}\n\n○b.{90°+360°n,270°+360°n, where n is any integer}\n\n○c.{90°+180°n,270°+180°n, where n is any integer}\n\n○d.{90°+360°n, where n is any integer}

Answer

Explanation:

Step1: Solve for (\csc\theta)

Given (\csc\theta - 1=0), add (1) to both sides. (\csc\theta=1)

Step2: Use the reciprocal identity (\csc\theta=\frac{1}{\sin\theta})

Since (\csc\theta = 1), then (\frac{1}{\sin\theta}=1), which implies (\sin\theta = 1).

Step3: Find the principal - value solution

We know that (\sin\theta = 1) when (\theta = 90^{\circ}) (because (\sin90^{\circ}=1)).

Step4: Use the period of the sine function

The period of the sine function (y = \sin\theta) is (360^{\circ}). The general solution of the equation (\sin\theta=\sin\alpha) is (\theta=\alpha + 360^{\circ}n), where (n\in\mathbb{Z}). Here (\alpha = 90^{\circ}), so (\theta=90^{\circ}+360^{\circ}n), (n\in\mathbb{Z}).

Answer:

D. ({90^{\circ}+360^{\circ}n,\text{ where }n\text{ is any integer}})