12. Without using a calculator, determine two angles between 0^{circ} and 360^{circ} that have a cosecant of -frac{2}{sqrt{3}}. Show your thinking on the grid below. (4 KU)

Question

Accepted Answer

Step:1 ：Since the cosecant is the reciprocal of the sine function, we need to find two angles with a sine of -frac{sqrt{3}}{2}. We know that sine is negative in the third and fourth quadrants.Step:2 ：First, let&#x27;s find the reference angle, which is the angle with a sine of frac{sqrt{3}}{2}. The reference angle is approximately 60^circ.Step:3 ：Now, we need to find the angles in the third and fourth quadrants with this reference angle. The angles are 240^circ and 300^circ.Step:4 ：(boxed{240^circ, 300^circ})

Answer

Step: 1 ：Since the cosecant is the reciprocal of the sine function, we need to find two angles with a sine of -frac{sqrt{3}}{2}. We know that sine is negative in the third and fourth quadrants.Step: 2 ：First, let&#x27;s find the reference angle, which is the angle with a sine of frac{sqrt{3}}{2}. The reference angle is approximately 60^circ.Step: 3 ：Now, we need to find the angles in the third and fourth quadrants with this reference angle. The angles are 240^circ and 300^circ.Step: 4 ：(boxed{240^circ, 300^circ})

12. Without using a calculator, determine two angles between $0^{\circ}$ and $360^{\circ}$ that have a cosecant of $-\frac{2}{\sqrt{3}}$. Show your thinking on the grid below. (4 KU)

Answer

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