Question

Find the values of θ for which each equation is true.3. sin θ = 04, cos θ = 1

Answer 1

Answer:
`\begin{gathered} 3)\text{ }\theta\text{ = }\ldots-270^0,90^0,\text{ 450}^0\ldots\ldots \\ 4)\text{ }\theta\text{ = }\ldots.\text{-360}^0,\text{ 0, 36}0^0\ldots. \end{gathered}`Explanations:3) Sin θ = 1

To find the values of θ

`\theta\text{ = }\sin ^(-1)1`
`\theta\text{ = }((4n+1)\pi)/(2)\text{ for n }\in\text{ Z},\text{ that is, n is an integer}`

Let us pick some values of n, n = ..... -1, 0, 1.....

`\begin{gathered} \theta=\ldots\ldots,\text{ }(-3\pi)/(2),(\pi)/(2),(5\pi)/(2),\ldots\ldots \\ \theta\text{ = }\ldots-270^0,90^0,\text{ 450}^0\ldots\ldots \end{gathered}`4) Cos θ = 1
`\theta=\cos ^(-1)(1)`
`\begin{gathered} \theta\text{ = 2n}\pi\text{ where n is an integer} \\ \text{For n = }\ldots.-1,\text{ 0, 1}\ldots.. \\ \theta\text{ = }\ldots\ldots.,\text{-2}\pi,\text{ 0, 2}\pi,\ldots\ldots \\ \theta\text{ = }\ldots.\text{-360}^0,\text{ 0, 36}0^0\ldots. \end{gathered}`