How do you solve sin(x)-cos(x/3)=0?

2 Answers
Sean
May 17, 2018

#x=(3pi)/8#

Explanation:

.

#sinx-cos(x/3)=0#

#sinx=cos(x/3)#

We know:

#sin(pi/2-theta)=costheta#

Therefore,

#sin(pi/2-x/3)=cos(x/3)#

#x=pi/2-x/3#

#x+x/3=pi/2#

#6x+2x=3pi#

#8x=3pi#

#x=(3pi)/8#

Nghi N
May 17, 2018

#x = (3pi)/8 + (3kpi)/2#
#x = (3pi)/4 + 3kpi#

Explanation:

#sin x = cos (x/3)#
#cos (pi/2 - x) = cos (x/3)#
Unit circle and property of cos function -->
#pi/2 - x = +- x/3#
a. #pi/2 - x = x/3#
#x + x/3 = pi/2#
#(4x)/3 = pi/2 + 2kpi#
#x = (3pi)/8 + (3kpi)/2#
b. #pi/2 - x = - x/3#
#x - x/3 = pi/2#
#(2x/3) = pi /2 + 2kpi#
#x = (3pi)/4 + 3kpi#

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