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How do you solve $cos^2 theta-sin^2 theta +sin theta=0$ ?

1 Answer

Jun 4, 2018

$theta = -30^circ + 360^circ k quad$ or

$theta = -150^circ + 360^circ k$ or

$theta = 90^circ + 360^circ k$

all for integer $k$ .

Explanation:

I think I just did this one recently.

$cos ^2 theta - sin ^2 theta + sin theta = 0$

$1 - sin ^2 theta - sin ^2 theta + sin theta = 0$

$2 sin theta - sin theta -1 = 0$

$(2 sin theta +1 ) (sin theta - 1) = 0$

$sin theta = -1/2 or sin theta = 1$

$theta = -30^circ + 360^circ k quad$ or

$theta = -150^circ + 360^circ k$ or

$theta = 90^circ + 360^circ k$

all for integer $k$ .

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