Find all solutions of the following equation in the interval (0, 2pi)
Equation: -cos(x)= sqrt2/ 2. It should ahve two answers. thanks.
2006-09-14 16:59:21 · 4 answers · asked by Slevin Kelevra 2 in Science & Mathematics ➔ Mathematics
-cos x = sqrt(2)/2
cos x = -1/(Sqrt(2)
we know cos pi/4 = 1/sqrt(2)
cos is -ve in 2nd and 3rd quadrant
so x = pi + pi/4 or pi-pi/4(as cos(pi-x) = - cos x also cos(pi+x) = - cos x
so 2 solutions are 3pi/4 and 5pi/4
2006-09-14 17:04:03 · answer #1 · answered by Mein Hoon Na 7 · 1⤊ 1⤋
Draw a unit circle. It is obvious by inspection that the middle point of the arc in each quadrant is a nominal solution. Since one takes the positive root, and a negative cosine is requested, the two points required are the ones in the second and third quadrants.
2006-09-15 00:03:30 · answer #2 · answered by Anonymous · 1⤊ 0⤋
There are 2 solutions, 3pi/4 and 5pi/4
2006-09-15 00:04:00 · answer #3 · answered by Steiner 7 · 0⤊ 1⤋
-cos(x) = sqrt(2)/2
cos(x) = -sqrt(2)/2
x = cos^(-1)(-sqrt(2)/2)
x = 135° or 225°
ANS : (3/4)pi or (5/4)pi
2006-09-15 01:10:50 · answer #4 · answered by Sherman81 6 · 0⤊ 0⤋