Question

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. sin 0 - 1 = 0 choose the correct answer below. a. {90° + 180°n, 270° + 180°n, where n is any integer} b. {90° + 180°n, where n is any integer} c. {90° + 360°n, where n is any integer} d. {90° + 360°n, 270° + 360°n, where n is any integer}

Explanation:

Step1: Solve the equation for \(\sin\theta\)

Given \(\sin\theta - 1=0\), add \(1\) to both sides:
\(\sin\theta=1\)

Step2: Recall the values of \(\theta\) for which \(\sin\theta = 1\)

We know that \(\sin\theta = 1\) when \(\theta = 90^{\circ}+360^{\circ}n\), where \(n\) is any integer (because the sine function has a period of \(360^{\circ}\)). The general solution of the equation \(\sin x = k\) is \(x=\sin^{- 1}(k)+360^{\circ}n\) or \(x = 180^{\circ}-\sin^{-1}(k)+360^{\circ}n\). For \(k = 1\), \(\sin^{-1}(1)=90^{\circ}\) and \(180^{\circ}-\sin^{-1}(1)=90^{\circ}\)

Answer:

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