In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.csc 17°

Verified step by step guidance

1. Understand that the cosecant function, \( \csc \theta \), is the reciprocal of the sine function, \( \sin \theta \). Therefore, \( \csc 17^\circ = \frac{1}{\sin 17^\circ} \).
2. Use a calculator to find \( \sin 17^\circ \). Ensure your calculator is set to degree mode.
3. Once you have the value of \( \sin 17^\circ \), take the reciprocal of this value to find \( \csc 17^\circ \).
4. Input \( \frac{1}{\sin 17^\circ} \) into the calculator to compute the value of \( \csc 17^\circ \).
5. Round the result to four decimal places as required by the problem.

Key Concepts

Cosecant Function

The cosecant function, denoted as csc, is the reciprocal of the sine function. It is defined as csc(θ) = 1/sin(θ). This means that to find the cosecant of an angle, you first need to calculate the sine of that angle and then take its reciprocal. Understanding this relationship is crucial for solving problems involving csc.

Using a Calculator for Trigonometric Functions

Calculators often have built-in functions for trigonometric calculations, including sine, cosine, and cosecant. To find csc(17°), you would first compute sin(17°) using the calculator and then take the reciprocal of that value. Familiarity with your calculator's functions and settings, such as ensuring it is in degree mode, is essential for accurate results.

Rounding and Precision

When calculating trigonometric values, rounding to a specific number of decimal places is important for precision. In this case, the problem specifies rounding to four decimal places. This involves determining the value accurately and then applying standard rounding rules to ensure the final answer meets the required precision.