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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 41
Chapter 1, Problem 41

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
tan 32.7°

Verified step by step guidance
1
Identify the trigonometric function to evaluate, which is the tangent of 32.7 degrees, written as \(\tan 32.7^\circ\).
Make sure your calculator is set to degree mode since the angle is given in degrees, not radians.
Input the angle 32.7 into the calculator and then use the tangent function key to find \(\tan 32.7^\circ\).
Read the value displayed on the calculator, which is the tangent of 32.7 degrees.
Round the result to four decimal places as required by the problem.

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Key Concepts

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

Understanding the Tangent Function

The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the adjacent side. It is a fundamental trigonometric function that relates an angle to a ratio of sides, often used to find slopes or angles in various applications.
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Introduction to Tangent Graph

Using a Calculator for Trigonometric Functions

Calculators can compute trigonometric values directly when the angle is input in the correct mode (degrees or radians). For this problem, ensure the calculator is set to degree mode before calculating tan 32.7°, to obtain an accurate decimal value.
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How to Use a Calculator for Trig Functions

Rounding to Four Decimal Places

After calculating the trigonometric value, rounding to four decimal places means limiting the result to four digits after the decimal point. This ensures precision and consistency in answers, which is important for clarity and comparison in mathematical problems.
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Example 1
Related Practice
Textbook Question

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

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Textbook Question

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

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In Exercises 41–43, find the exact value of each of the remaining trigonometric functions of θ.

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In Exercises 33–42, let sin t = a, cos t = b, and tan t = c. Write each expression in terms of a, b, and c.

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Textbook Question

In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places.

-5.2 radians

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In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.

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