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Ch. 1 - Angles and the Trigonometric Functions
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 3rd EditionCh. 1 - Angles and the Trigonometric FunctionsProblema 45
Capitolo 1, Problema 45

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
cos 𝜋/10

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1
Recognize that the problem asks for the value of the cosine function at the angle \( \frac{\pi}{10} \). This angle is in radians.
Recall that \( \pi \) radians is equivalent to 180 degrees, so \( \frac{\pi}{10} \) radians corresponds to \( \frac{180}{10} = 18 \) degrees.
Use a calculator set to radian mode to evaluate \( \cos\left(\frac{\pi}{10}\right) \). Make sure the calculator is in the correct mode (radians) before calculating.
Input the expression \( \cos\left(\frac{\pi}{10}\right) \) into the calculator. This can be done by entering \( \pi \) divided by 10, then applying the cosine function.
Record the value displayed by the calculator and round it to four decimal places as required.

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Radian Measure

Radian measure is a way to express angles based on the radius of a circle. One radian is the angle subtended by an arc equal in length to the radius. Understanding radians is essential because trigonometric functions often use radian inputs, such as π/10 in this problem.
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5:04
Converting between Degrees & Radians

Cosine Function

The cosine function relates an angle to the ratio of the adjacent side over the hypotenuse in a right triangle. It is periodic and defined for all real numbers, often evaluated using radians. Calculating cos(π/10) requires understanding how cosine behaves and how to use a calculator for precise values.
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5:53
Graph of Sine and Cosine Function

Using a Calculator for Trigonometric Values

Calculators can compute trigonometric functions to high precision, but the mode must be set correctly (radians vs degrees). For cos(π/10), ensure the calculator is in radian mode, input the value accurately, and round the result to four decimal places as required.
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4:45
How to Use a Calculator for Trig Functions
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