Trig Equation (1 Viewer)

js992 · Apr 20, 2010

This question is from 3U cambridge year 12.

$cos2\theta + 3 = 3sin2\theta\\ $Hint: Wrote 3 as 3cos^2\theta + 3 sin^2\theta\\ 0\leq \theta\leq 2\pi\\ $Solve for$ \theta$,$ giving solutions to the nearest minute$$

I have no idea how to do it

hscishard · Apr 20, 2010

If all else fails, use the long t formula. Lol

Drongoski · Apr 20, 2010

hscishard · Apr 20, 2010

Drongoski said:
$cos 2\theta\ + 3\ \ =\ \ 3sin2\theta \\ \\ \therefore \ \ cos^{2}\theta \ -\ sin^{2}\theta \ +\ 3sin^{2}\theta \ +\ 3cos^{2}\theta \ \ =\ \ 6\ sin\theta cos\theta \\ \\ \therefore\ \ 4cos^{2}\theta \ +\ 2sin^{2}\theta \ -\ 6sin\theta cos\theta \ \ =\ \ 0\\ \\ \therefore \ \ 2cos^{2} \theta \ +\ sin^{2}\theta \ -\ 3sin\theta cos\theta \ \ =\ \ 0\\ \\ \therefore \ \ (2cos\theta \ -\ sin\theta )(cos\theta \ -\ sin\theta )\ \ =\ \ 0\\ \\ \therefore \ \ tan\ \theta \ =\ 2\ \ \ or\ \ \ tan\ \theta \ =\ 1 \\ \\ \therefore \ \ \theta \ =\ 63\ 27'\ \ or\ \ 243^{\circ}\ 27'\ \ \ \ or\ \ 45^{\circ}\ \ or\ \ 225^{\circ}$

Nice. cos^2-sin^2, forgot about that. Thx

js992 · Apr 20, 2010

Ahhh, i got stuck before factorising cause i couldnt see what to do.

Thank you

Trig Equation (1 Viewer)

js992

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hscishard

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