Evaluate the trigonometric function using a calculator. Round your answers to four decimal places. $$ \csc \left(303^{\circ}\right)=\square $$

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UpStudy AI · Accepted Answer

To evaluate $$ \csc(303^\circ) $$, we can follow these steps:

1. **Recall the Definition:**
   $$
   \csc(\theta) = \frac{1}{\sin(\theta)}
   $$

2. **Find $$ \sin(303^\circ) $$:**
   - $$ 303^\circ $$ is in the **fourth quadrant**, where sine values are **negative**.
   - $$ 303^\circ = 270^\circ + 33^\circ $$, so:
     $$
     \sin(303^\circ) = -\cos(33^\circ)
     $$
   - Using a calculator:
     $$
     \cos(33^\circ) \approx 0.8387
     $$
     $$
     \sin(303^\circ) \approx -0.8387
     $$

3. **Calculate $$ \csc(303^\circ) $$:**
   $$
   \csc(303^\circ) = \frac{1}{\sin(303^\circ)} \approx \frac{1}{-0.8387} \approx -1.1918
   $$

**Final Answer:**
$$
\csc(303^\circ) \approx -1.1918
$$
$$ \csc(303^\circ) \approx -1.1918 $$

Evaluate the trigonometric function using a calculator. Round your answers to four decimal places. \( \csc \left(303^{\circ}\right)=\square \)

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