Question
solve the equation in the interval [0,2pi) tan (t/2)-sint=0
Answers
Steve
tan(t/2) - sint = 0
(1-cost)/sint = sint
1-cost = sin^2 t
1-cost = 1-cos^2 t
cost(1-cost) = 0
cost = 0 or 1
t = pi/2,pi,3pi/2
see
http://www.wolframalpha.com/input/?i=solve+tan%28t%2F2%29+%3D+sint+for+t%3D0..2pi
(1-cost)/sint = sint
1-cost = sin^2 t
1-cost = 1-cos^2 t
cost(1-cost) = 0
cost = 0 or 1
t = pi/2,pi,3pi/2
see
http://www.wolframalpha.com/input/?i=solve+tan%28t%2F2%29+%3D+sint+for+t%3D0..2pi