Textbook Question
Find the reference angle for each angle.
5π/4
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
Chapter 1, Problem 43
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 guidance1
Recall that the cosecant function is the reciprocal of the sine function. This means that \(\csc \theta = \frac{1}{\sin \theta}\).
Identify the angle given in the problem, which is \(17^\circ\).
Use a calculator to find the sine of \(17^\circ\). Make sure your calculator is set to degree mode before calculating \(\sin 17^\circ\).
Calculate the reciprocal of the sine value obtained: \(\csc 17^\circ = \frac{1}{\sin 17^\circ}\).
Round the result to four decimal places as requested.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Reciprocal Trigonometric Functions
The cosecant (csc) function is the reciprocal of the sine function, defined as csc θ = 1/sin θ. Understanding this relationship allows you to find csc values by first calculating sine values and then taking their reciprocals.
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Introduction to Trigonometric Functions
Using a Calculator for Trigonometric Values
Calculators can directly compute sine values for given angles in degrees or radians. To find csc 17°, first calculate sin 17° using the calculator, then take the reciprocal to get csc 17°, ensuring the calculator is set to degree mode.
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Rounding and Precision in Trigonometric Calculations
When reporting trigonometric values, it is important to round the result to the specified number of decimal places, here four. This ensures consistency and accuracy in answers, especially when using approximate decimal values from calculators.
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Related Practice
Textbook Question
In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
3𝜋/4
Textbook Question
In Exercises 41–43, find the exact value of each of the remaining trigonometric functions of θ.
cos θ = 2/5, sin θ < 0
Textbook Question
In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
7𝜋/6
Textbook Question
In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
7𝜋/4
Textbook Question
In Exercises 44–48, find the reference angle for each angle.
265°
6
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