Questions: csc(-270°)

Transcript text: $\csc \left(-270^{\circ}\right)$

Solution

Solution Steps

To solve for $\csc \left(-270^{\circ}\right)$, we need to understand the relationship between the cosecant function and the sine function. The cosecant function is the reciprocal of the sine function. Therefore, we first need to find $\sin \left(-270^{\circ}\right)$ and then take its reciprocal.

Step 1: Convert Degrees to Radians

To find $\csc \left(-270^{\circ}\right)$, we first convert the angle from degrees to radians: \[ -270^{\circ} = -\frac{3\pi}{2} \text{ radians} \]

Step 2: Calculate the Sine of the Angle

Next, we calculate $\sin \left(-\frac{3\pi}{2}\right)$: \[ \sin \left(-\frac{3\pi}{2}\right) = 1 \]

Step 3: Calculate the Cosecant

The cosecant function is the reciprocal of the sine function: \[ \csc \left(-\frac{3\pi}{2}\right) = \frac{1}{\sin \left(-\frac{3\pi}{2}\right)} = \frac{1}{1} = 1 \]

Final Answer

\[ \boxed{\csc \left(-270^{\circ}\right) = 1} \]

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