Question
Determine the total number of solutions for the given equation: tan(2θ-pi/2)=1 on the interval [0, 2pi]
Answers
Damon
sin (2θ-pi/2) / cos (2θ-pi/2) = 1
sin (2θ-pi/2) = cos (2θ-pi/2)
that happens when we are 45 degrees from any axis in quadrants 1 or 3
(2θ-pi/2) = pi/4
2 θ = 3 pi/4
θ = 3 pi/8
(2θ-pi/2) = 5 pi/4
2θ = 7 pi/4
θ = 7 pi/8
(2θ-pi/2)= 2 pi + pi/4 = 11 pi/4
θ =11 pi/8
continue until θ is > 2 pi
(2θ-pi/2) = 3 pi + pi/4
sin (2θ-pi/2) = cos (2θ-pi/2)
that happens when we are 45 degrees from any axis in quadrants 1 or 3
(2θ-pi/2) = pi/4
2 θ = 3 pi/4
θ = 3 pi/8
(2θ-pi/2) = 5 pi/4
2θ = 7 pi/4
θ = 7 pi/8
(2θ-pi/2)= 2 pi + pi/4 = 11 pi/4
θ =11 pi/8
continue until θ is > 2 pi
(2θ-pi/2) = 3 pi + pi/4