Question #94f10

2 Answers
Mar 28, 2016

Answer:

#theta = (1/3)(+-(2n+1)pi-pi/2)#, n = 0, 1, 2, 3..= #pi/6, 5pi/6, 9pi/6, 13pi/6, ...#. The negative solutions are #-3pi/6, -7pi/6, -11pi/6, ....#

Explanation:

The general value of #cos^(-1)(-1)# = an odd multiple of #pi#.

So, #3theta+pi/2# = an odd multiple of #pi# = #+-(2n+1)pi#, n = 0, 1, 2, 3, ...

Positive solutions are #pi/6, 5pi/6, 9pi/6, 13pi/6, ...#
The negative solutions are #-3pi/6, -7pi/6, -11pi/6, ....#

Mar 28, 2016

Answer:

#t = pi/2 + k.pi#

Explanation:

Trig unit circle gives -->
#cos (3t + pi/2) = - 1 = cos pi#
#3t + pi/2 = +- pi#
a. #3t = pi - pi/2 = pi/2#. ---># t = (3pi)/2 #
b. #3t = -pi - pi/2 = -(3pi)/2#, or #(pi/2)# --> co-terminal
General answers:
#t = pi/2 + k.pi#