Question #e9d6f

1 Answer
Sean
Dec 3, 2017

#292.5=arctan2.4142#

#292.5=arctan0.4142#

Explanation:

Call #x = tan 292.5#
#tan2(292.5)=tan585=tan(135 + 360)=tan(135)=-tan45=- 1#

Using trigonometric identity:# tan2x=(2tanx)/(1-tan^2 x)#

#- 1 = (2x)/(1 - x^2) # -> #x^2 - 2x - 1 = 0#

#x=(2+-sqrt(4+4))/2=(2+-2sqrt2)/2=1+-sqrt2=#

#x=tan292.5=2.4142#, then #292.5=arctan2.4142#

#x=tan292.5=-0.4142#, then #292.5=arctan0.4142#

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