Find all values for t in the interval [0, 2π) satisfying cos(-t)=sin(t)
2006-12-02 11:42:47 · 5 answers · asked by Sparkles 3 in Science & Mathematics ➔ Mathematics
cos(-t)=sin(t)
cos(-t) = cos(t) for all t
So cos(t) = sin(t)
So 1 = sin(t)/cos(t)
ie tan(t) = 1
t = π/4, 5π/4 for t in the interval [0, 2π)
2006-12-02 11:49:07 · answer #1 · answered by Wal C 6 · 0⤊ 1⤋
Cos is an even function---> cos(-t)=cos(t)
when cos(t)=sin(t)
t=1/4pi (sqrt(2)/2)
t=5/4pi (-sqrt(2)/2)
2006-12-02 19:54:25 · answer #2 · answered by cnt 2 · 1⤊ 0⤋
cos(-t) = sin(t)
sin(t) = cos(t - (pi/2))
cos(-t) = cos(t - (pi/2))
-t = t - (pi/2))
-2t = (-pi/2)
t = (pi/4) or (5pi/4)
2006-12-02 21:48:06 · answer #3 · answered by Sherman81 6 · 1⤊ 0⤋
cos(-t)=cost=sint
t=pi/4 and 7pi/4
2006-12-02 19:52:44 · answer #4 · answered by raj 7 · 0⤊ 1⤋
Ï/4 and -3Ï/4
sin(Ï/4)=cos(Ï/4)=cos(-Ï/4)
sin(-3Ï/4)=cos(3Ï/4)
2006-12-02 20:03:11 · answer #5 · answered by albert 5 · 0⤊ 1⤋