does anyone know how to find multiple solutions for such a equation? thank youu
View attachment 33719
Is this an advance question?
I believe microsoft calculator can solve these types of question
The general solution for:
cos(theta) = a
is
2*n*pi +/- alpha
(1)
______________________
sin theta = a
is
theta = n*pi +(-1)^n * alpha
(2)
_______________________
tan(theta) = a
is
theta = n*pi + alpha
(3)
____________________________
Of course you are not going to be able to apply theorem
(1)/(2)/(3) in these types of questions because of the coefficent of t is 2pi/3 not 1.
So let u = 2pi/3 * t. With this substitution you can now apply the theorem as the coefficent is now 1 which is coefficent of theta.
So you have
u = n*pi +(-1)^n * alpha # note alpha = sin^-1(a)
2pi/3 * t = n*pi +(-1)^n * alpha # make t the subject and your done.
Note: To save time in a exam you don't need to actually substitute u.
