SOLUTION: Dear Sir/ Madam; A pleasant day! Can you please help me answer this problem involving coordinates of point P(θ) on the Unit circle. Let the initial side and the

Algebra ->  Trigonometry-basics -> SOLUTION: Dear Sir/ Madam; A pleasant day! Can you please help me answer this problem involving coordinates of point P(θ) on the Unit circle. Let the initial side and the      Log On


   

Question 826526: Dear Sir/ Madam;
A pleasant day! Can you please help me answer this problem involving coordinates of point P(θ) on the Unit circle.
Let the initial side and the terminal side of an angle be in standard position which intersects the unit circle at P(1,0) and Q(x,y). Find the missing coordinate in the points (1/4 , y).
Thanks for your help!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
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.

To find the sin of the angle, we will use sin%5E2%28x%29=1-cos%5E2%28x%29:
sin%5E2%28x%29+=+1-%281%2F4%29%5E2
Solving for sin(x):
sin%5E2%28x%29+=+1-1%2F16
sin%5E2%28x%29+=+16%2F16-1%2F16
sin%5E2%28x%29+=+15%2F16
sqrt%28sin%5E2%28x%29%29+=+0%2B-sqrt%2815%2F16%29
(Note: Algebra.com will not let me use a + 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%28x%29+=+0%2B-sqrt%2815%29%2Fsqrt%2816%29
sin%28x%29+=+0%2B-sqrt%2815%29%2F4
which is short for:
sin%28x%29+=+sqrt%2815%29%2F4 or sin%28x%29+=+-sqrt%2815%29%2F4
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%2815%29%2F4) and (1/4, -sqrt%2815%29%2F4)