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SolCon

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I have 2 trigno "solve the equation for" problems which I am having difficulty with.

Q.1) This came in 2 parts. I've done the first part but I'll post it anyway as it is important for the next part (where I'm having difficulty).

i) Show that equation 4sin^4[tex]\theta[/tex] + 5=7cos^2[tex]\theta[/tex] may be written as 4x^2+7x-2=0 where x=sin^2[tex]\theta[/tex].

I got this part done.

ii) then it says to solve the equation 4sin^4[tex]\theta[/tex] + 5=7cos^2[tex]\theta[/tex] for 0 <= [tex]\theta[/tex] <= 360.

I tried factorising the proven equation (with the x only) and received 2 values of x i.e x=1/4

and x=-2. The x=-2 is undefined but for the x=1/4, this seems to be incorrect but I do not know why.

Q.2) This is similar to part II of the first question. It says to find all the values of x in the interval 0<=x<=180 which satisfies the equation sin3x+2cos3x=0.

For this one, I simply shifted 2cos3x to the other side and simplified it as tan3x=-2. Is this correct? If it is, I'm still getting wrong values. Do we take this as x=tan^-1(-2/3) or some other way? If the former, then the value I get is -33.69 which seems to be incorrect (correct base value is 38.9).

Any help with both these questions?