Question 826526
First of all, the coordinates of points on a unit circle are the cos and sin of the angle in standard position whose terminal side passes through that point. So the 1/4 in (1/4, y) is the cos of the angle in question and the y is the sin of that same angle.<br>
To find the sin of the angle, we will use {{{sin^2(x)=1-cos^2(x)}}}:
{{{sin^2(x) = 1-(1/4)^2}}}
Solving for sin(x):
{{{sin^2(x) = 1-1/16}}}
{{{sin^2(x) = 16/16-1/16}}}
{{{sin^2(x) = 15/16}}}
{{{sqrt(sin^2(x)) = 0+-sqrt(15/16)}}}
(Note: Algebra.com will not let me use a <u>+</u> sign in a formula without a number in front of it. That is why there is a zero. You do not and should not use the zero yourself.)
{{{sin(x) = 0+-sqrt(15)/sqrt(16)}}}
{{{sin(x) = 0+-sqrt(15)/4}}}
which is short for:
{{{sin(x) = sqrt(15)/4}}} or {{{sin(x) = -sqrt(15)/4}}}
Remembering that these sin's are the possible y coordinates, these are our answers. There are two points on the unit circle with an x coordinate of 1/4:
(1/4, {{{sqrt(15)/4}}}) and (1/4, {{{-sqrt(15)/4}}})