Remember the double angle identity: sin(2a) = 2*sin(a)*cos(a).
4sin(2x)+4cos(x)=0 --->divide out the like term (4) ---> 4(sin(2x)+cos(x)) = 0 ---> (divide both sides by 4)---> sin(2x) + cos(x) = 0 (use the double angle identity.
2sin(x)cos(x) + cos(x) = 0 ---> factor out like terms (cos(x) ---> cos(x)(2sin(x)+1) = 0 Now use the zero product rule.
cos(x) = 0 which for the stated range is 90 degrees or pi/2.
2sin(x) + 1 = 0 ---> 2sin(x) = -1 ---> sin(x) = -1/2 which is 210 degrees or 7pi/6 in the stated range.
Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)
(