Question

TRIGONOMETRY Given a unite circle what is the value for y?

Answer 1

Let's put more details in the given figure:

To find y, we will be using the Pythagorean Theorem.

`\begin{gathered} c^2=a^2+b^2 \\ \text{r}^2=x^2+y^2 \\ \end{gathered}`

Where,

r = radius

x = 1/3

y = uknown

We get,

`\text{r}^2=x^2+y^2`
`\begin{gathered} y^2\text{ = r}^2\text{ - }x^2 \\ y^{}\text{ = }\sqrt{\text{r}^2\text{ - }x^2} \end{gathered}`
`\text{ y = }\sqrt[]{1^2-((1)/(2))^2}\text{ = }\sqrt[]{1\text{ - }(1)/(4)}`
`\text{ y = }\sqrt[]{(3)/(4)}\text{ = }\frac{\sqrt[]{3}}{\sqrt[]{4}}`
`\text{ y = }\frac{\sqrt[]{3}}{2}`

Therefore, the answer is:

`\text{ y = }\frac{\sqrt[]{3}}{2}`