Find #tan (x/2)# by calculator.
tan x = 0.366 --> Calculator gives --> 2 solutions -->
a. #x = 20^@10# --># x/2 = 10^@05# --> #tan (x/2) = 0.177#
b. #x = 20.10 + 180 = 200^@10# --> #x/2 = 100^@05#
#tan (x/2) = tan (100.05) = - 5.64#
Note. You can also evaluate #tan (x/2)# by using trig formula:
#tan x = (2tan (x/2))/(1 - tan^2 (x/2)) = 0.366#
Solve this quadratic equation for #tan (x/2) = t#
#0.37t^2 + 2t - 0,37 = 0#
#D = d^2 = b^2 - 4ac = 4 + 0.55 = 4.55# --> #d = +- 2.13#
There are 2 real roots:
#tan (x/2) = -b/(2a) +- d/(2a) = -2/0.74 +- 2.13/.74 = - 2.70 +- 2.88#
#tan (x/2) = t = - 2.70 - 2.88 = - 5.58# OK
#tan (x/2) = t = - 2.70 + 2.88 = 0.18 # OK
