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Ch. 1 - Angles and the Trigonometric Functions
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Not the one you use?Change textbook
All textbooksBlitzer 3rd EditionCh. 1 - Angles and the Trigonometric FunctionsProblem 45
Chapter 1, Problem 45

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

Verified step by step guidance
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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 Ο€/10 in this problem.
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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(Ο€/10) requires understanding how cosine behaves and how to use a calculator for precise values.
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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(Ο€/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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How to Use a Calculator for Trig Functions
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.

-2πœ‹/3

3
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Textbook Question

In Exercises 35–60, find the reference angle for each angle.

-150Β°

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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.

-5πœ‹/6

1
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Textbook Question

In Exercises 44–48, find the reference angle for each angle.

-410Β°

4
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Textbook Question
In Exercises 45–52, graph two periods of each function.y = 2 tan(x βˆ’ Ο€/6) + 1
Textbook Question

In Exercises 44–48, find the reference angle for each angle.

265Β°

6
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