Domanda del libro di testo
Find the reference angle for each angle.
5π/4
591
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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TOC.tableOfContents
Capitolo 1, Problema 43
In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
csc 17°
Guida verificata passo dopo passo1
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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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.
Video consigliato:
Percorso guidato
6:04
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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Percorso guidato
4:45How to Use a Calculator for Trig Functions
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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Percorso guidato
4:45How to Use a Calculator for Trig Functions
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In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
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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.
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In Exercises 44–48, find the reference angle for each angle.
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