How do you find the solution to #sintheta+3=5sintheta# if #0<=theta<2pi#?
1 Answer
Jul 14, 2017
Explanation:
We want to solve:
# sin theta + 3 = 5sin theta # where#theta in [0,2pi)#
We can write this as:
# \ \ 4sin theta = 3 #
# :. sin theta = 3/4 #
If we consider the graph of
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# sin theta = 3/4 => #
# " " theta_1 = arcsin(3/4)# (the fundamental value)
# " " \ \ \ = 0.848^r# (3dp)
So the two solutions in the specified range are:
# theta = theta_1, pi-theta_1 #
# \ \ = 0.848^r, 2.294^r #