Question

Which has a terminal point of (square root 2/2 and square root 2/2). What is the terminal point of 5pi/4?

Answer 1

`\text{(-}\frac{\sqrt[]{2}}{2},\text{ -}\frac{\sqrt[]{2}}{2})\text{ (option C)}`

Step-by-step explanation:
`\begin{gathered} \text{terminal point of }(\pi)/(4)\text{ is (}\frac{\sqrt[]{2}}{2},\text{ }\frac{\sqrt[]{2}}{2}) \\ \text{ }(\pi)/(4)\text{ in degr}es\text{ = 45}\degree \end{gathered}`

To find 5π/4 as terminal point, we will take the angle as 5π/4

The first coordinate is the x coordinate = cos θ

The second coordinate is the y coordinate = sin θ

`\begin{gathered} We\text{ n}eed\text{ to convert the angle to degre}e\colon \\ 1\pi\text{ rad = 180}\degree \\ (5\pi)/(4)\text{ rad = 225}\degree \\ \\ sin\text{ is negative in third quadrant} \\ 225\text{ - 180 = 45} \\ \sin \text{ 45 = }\frac{\sqrt[]{2}}{2} \\ \\ \sin \text{ 225}\degree\text{ =- }\frac{\sqrt[]{2}}{2} \end{gathered}`
`\begin{gathered} \theta\text{ = 225}\degree\text{ }is\text{ in third quadrant} \\ \\ 180\text{ -225 = 45}\degree \\ \cos \text{ 45}\degree\text{ = }\frac{\sqrt[]{2}}{2} \\ \text{ 225 is negative in third quadrant} \\ \\ \cos \text{ 225}\degree\text{ =- }\frac{\sqrt[]{2}}{2} \end{gathered}`

Hence, the terminal of 5π/4:

`\text{(-}\frac{\sqrt[]{2}}{2},\text{ -}\frac{\sqrt[]{2}}{2})\text{ (option C)}`