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a = \frac6-4 = -\frac32 - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The solutions for \(\theta\) in the interval \([0^\circ, 360^\circ]\) are:

📌 \theta = 30^\circ \quad \text{and} \quad \theta = 150^\circ.

📌 Next, consider the case where \(\cos(\theta) = 0\). This occurs at:

📌 \theta = 90^\circ \quad \text{and} \quad \theta = 270^\circ.

📌 Checking these values in the original equation, we find \(\sin(180^\circ) = 0\) and \(\sin(540^\circ) = 0\), both equal to \(\cos(90^\circ) = 0\) and \(\cos(270^\circ) = 0\), so they are valid.

📌 Thus, the complete set of solutions is:

📌 \(\theta = 30^\circ, 90^\circ, 150^\circ, 270^\circ\).

📌 \boxed{30^\circ, 90^\circ, 150^\circ, 270^\circ}

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Subtract the second from the third:
Substitute \( b = -9a \) into \( 6a + b = \frac{7}{2} \):
6a - 9a = \frac{7}{2} \implies -3a = \frac{7}{2} \implies a = -\frac{7...
Now find \( b \):
b = -9a = -9 \left(-\frac{7}{6}\right) = \frac{63}{6} = \frac{21}{2}
Substitute \( a \) and \( b \) into \( 7a + 3b + c = -4 \):
7\left(-\frac{7}{6}\right) + 3\left(\frac{21}{2}\right) + c = -4
-\frac{49}{6} + \frac{63}{2} + c = -4
Convert to a common denominator:
-\frac{49}{6} + \frac{189}{6} + c = -4

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