SOLUTION: If the equations y = sin x and y = cos x are both graphed on the same xy-axis system, the curves will intersect many times. Find coordinates for at least two intersection points.

Algebra ->  Trigonometry-basics -> SOLUTION: If the equations y = sin x and y = cos x are both graphed on the same xy-axis system, the curves will intersect many times. Find coordinates for at least two intersection points.       Log On


   

Question 1172993: If the equations y = sin x and y = cos x are both graphed on the same xy-axis system, the curves will intersect many times. Find coordinates for at least two intersection points.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


They intersect when sin(x) = cos(x)...

which is when sin(x)/cos(x) = tan(x) = 1...

which is when the angle x is 45 degrees in quadrant I or when it is 225 degrees in quadrant III.

They also intersect when the angle is any multiple of 360 degrees more than either 45 degrees or 225 degrees.

At 45 degrees, sin%28x%29+=+cos%28x%29+=+sqrt%282%29%2F2

At 225 degrees, sin%28x%29+=+cos%28x%29+=+-sqrt%282%29%2F2

ANSWERS (angles in degrees):
(45, sqrt(2)/2); (225, -sqrt(2)/2)