questions on 8.4 73 & 81
for 73, i am not seeing where the 1.2059 + k*pi value for tan x came from. Could someone help me w/ this.
Also, for 81, am i not allowed to say sin^2(x) + 3*cos^2(x) = 0 is the same as
1 - cos^2(x) + 3*cos^2(x) = 0, which changes to 1 - 2*cos^2(x) = 0, and in turn simplifies to cos (x) = +/- (sqrt(2))/2. This would indeed have a solution, as opposed to the book. Would someone support this?
Also, for 81, am i not allowed to say sin^2(x) + 3*cos^2(x) = 0 is the same as
1 - cos^2(x) + 3*cos^2(x) = 0, which changes to 1 - 2*cos^2(x) = 0, and in turn simplifies to cos (x) = +/- (sqrt(2))/2. This would indeed have a solution, as opposed to the book. Would someone support this?
posted by battlejoe18 at 4:46 PM
3 Comments:
Your thinking is right but your sign is wrong. It would change to 1+cos^2(x)=0. When you solve this you end up taking the squareroot of a negative number which yields an imaginary number. This is why the book says no solution.
same problem i have trouble with... 73
solution to #73:
4sin(x)tan(x)-3tan(x)+20sin(x)-15=0
(4sin(x)tan(x)-3tan(x))+(20sin(x)-15)=0
tan(x)*(4sin(x)-3)+5*(4sin(x)-3)=0
(tan(x)+5)*(4sin(x)-3)=0
tan(x)=5 or 4sin(x)-3=0
x=1.768, 4.909, .8481, 2.2935
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