Question

What are the coordinates of the point that corresponds to -7x/4 on the unit circle

Answer 1

This is a problem of intersection. So, we have two equations, first of all we have a straight line and the second equation is a circle with ratio equal to 1. Therefore, in a mathematical language this is established as follows:

(1)
`y = (-7x)/(4)`
(2)
`x^(2)+y^(2)=1`

We introduce (1) into (2):


`x^(2)+((-7x)/(4))^(2)=1`

`x^(2)+(49x)/(16)^(2)=1`

`65x^(2)=16`

There are two values, namely:


`\left \{ {{x_(1) = +0.4961 } \atop {x_(2) = -0.4961 }} \right.`

Then, substituing these values in the first (1) equation, we find:


`\left \{ {{y_(1) = -0.8681 } \atop {y_(2) = +0.8681 }} \right.`

Finally, the points are two:


`P_(1)=(0.4961,-0.8681)`

`P_(2)=(-0.4961,0.8681)`