Homework 75 More Tri www.webassign net/webStudent As gr rent Responses, brit ein

Question

Homework 75 More Tri www.webassign net/webStudent As gr rent Responses, brit eing121 349 1 : Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2m). (Enter your i separated list. sin(28) + sinte) 25 -1 points SPreCalc7 7.5044 Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2T). (Enter your separated list.) tan()-sin(e)- Need Help? linui 26. 1 points SPreCact 7.5 046 Use a Double or Half-Angle Formula to solve the equation in the interval [0, 2n). (Enter your separated list.) tante) + cot(e) -4 sin(29) Need Help? ReadH cha

Explanation / Answer

We have given sin(2)+sin()=0 and interval [0,2pi)

using double angles formula sin(2)=2sin()cos()

sin(2)+sin()=0

2sin()cos()+sin()=0

sin()(2cos()+1)=0

sin()=0 or cos()=-1/2

=0,pi or =2pi/3,4pi/3

=0,pi,2pi/3,4pi/3

25) We have given tan(/2)-sin()=0 and interval [0,2pi)

using half angle formula tan(/2)=[1-cos()]/sin()

tan(/2)-sin()=0

[1-cos()]/sin()-sin()=0

1-cos()-sin2()=0

1-sin2()-cos()=0

plug 1-sin2()=cos2()

cos2()-cos()=0

cos()(cos()-1)=0

cos()=0 or cos()=1

=pi/2,3pi/2 or =0

=pi/2,3pi/2,0

26) We have given tan()+cot()=4sin(2) and interval [0,2pi)

tan()+cot()=4sin(2)

tan()+cot()-4sin(2)=0

sin()/cos()+cos()/sin()-4sin(2)=0

[sin2()+cos2()-4sin(2)*cos()sin()]/cos()sin()=0

[sin2()+cos2()-4sin(2)*cos()sin()]=0

plug this sin2()+cos2()=1 and cos()sin()=sin(2)/2 into above equation

[1-4sin(2)*sin(2)/2]=0

1-2sin2(2)=0

sin2(2)=1/2

sin(2)=1/sqrt(2) or sin(2)=-1/sqrt(2)

2=pi/4,3pi/4 or 2=5pi/4,7pi/4

=pi/8,3pi/8 or =5pi/8,7pi/8

=pi/8,3pi/8,5pi/8,7pi/8

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