How do you solve #cosx(tanx-sqrt3)=0# and find all solutions in the interval #0<=x<360#?

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How do you solve #cosx(tanx-sqrt3)=0# and find all solutions in the interval #0<=x<360#?

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Answer 1 · 2017-07-04T21:47:47

#pi/3; pi/2; (4pi)/3, (3pi)/2#

Explanation:

#f(x) = cos x(tan x - sqrt3) = 0#
Either factor should be zero.
a. #cos x = 0# --> Unit circle gives -->
#x = pi/2# and #x = (3pi)/2#
b. #tan x = sqrt3# --> trig table and unit circle give -->
#x = pi/3# and #x = pi/3 + pi = (4pi)/3#

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How do you solve #cosx(tanx-sqrt3)=0# and find all solutions in the interval #0<=x<360#?

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