How do you solve #2cos^2 theta + cos theta -1 = 0#?

1 Answer
Sep 15, 2016

#(1 + 2k)pi; pi/3 + 2kpi; (5pi)/3 + 2kpi#

Explanation:

Solve the quadratic equation for cos t.
#f(t) = 2cos^2 t + cos t - 1 = 0#
Since a - b + c = 0, use shortcut. The 2 real roots are:
cos t = -1 and #cos t = -c/a = 1/2#
Use trig table of special arcs and unit circle -->

a. cos t = -1 --> #t = pi + 2kpi#
General answers: #t = (1 + 2k)pi#
b. #cos t = 1/2# --># t = +- pi/3 + 2kpi#
arc #(-pi)/3# and arc #(5pi)/3# are co-terminal.
General answers:
#(1 + 2k)pi#
#pi/3 + 2kpi#
#(5pi)/3 + 2kpi#