Question #23b7a

2 Answers
Jun 21, 2017

theta = pi/30 + (2pi)/5 * n , (11pi)/30 + (2pi)/5 * n , n=0,1,2,3,...

Explanation:

cos 5theta = sqrt3/2

5theta = cos^(-1)(sqrt3/2)

5theta = 1/6 pi, 11/6 pi, 13/6 pi, 23/6 pi, 25/6 pi, 35/6 pi...

theta = 1/30 pi, 11/30 pi, 13/30 pi, 23/30 pi, 25/30 pi, 35/30 pi...

we can divide into 2 type of sequences.
theta = 1/30 pi, 13/30 pi, 25/30 pi,... ->i
theta = 1/30 pi, 1/30 pi + 12/30 pi, 1/30 pi + 24/30 pi,...
theta = 1/30 pi + 12/30 n * pi

theta = 1/30 pi + 2/5 n * pi, n=0,1,2,3,...

theta = pi/30 + (2pi)/5 * n, n=0,1,2,3,...

theta = 11/30 pi, 23/30 pi, 35/30 pi,... ->ii
theta = 11/30 pi, 11/30 pi + 12/30 pi, 11/30 pi + 24/30 pi,...
theta = 11/30 pi + 12/30 n * pi,

theta = 11/30 pi + 2/5 n * pi, n=0,1,2,3,...

theta = (11pi)/30 + (2pi)/5 * n , n=0,1,2,3,...

Jun 21, 2017

t = +- pi/30 + (2kpi)/5

Explanation:

cos 5t = sqrt3/2
Use trig table and unit circle:
5t = +- pi/6 + 2kpi
General answer:
t = +- pi/30 + (2kpi)/5
If you don't want a negative arc answer, you may replace the arc
(-pi/30) by the co-terminal arc (59pi)/30.
General answer:
t = pi/30 + (2kpi)/5
t = (59pi)/30 + (2kpi)/5