Textbook Question
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.
sin(-t - 2𝜋) - cos(-t - 4𝜋) - tan(-t - 𝜋)
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
Chapter 1, Problem 39
In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
sin 38°
Verified step by step guidance1
Identify the trigonometric function to evaluate, which is \(\sin 38^\circ\).
Make sure your calculator is set to degree mode since the angle is given in degrees.
Input the angle 38 into the sine function on your calculator, i.e., press the sine button and then enter 38.
Read the value displayed on the calculator, which is the sine of 38 degrees.
Round the result 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.
Understanding the Sine Function
The sine function relates an angle in a right triangle to the ratio of the length of the side opposite the angle to the hypotenuse. It is a fundamental trigonometric function used to find unknown side lengths or angles in triangles.
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5:53
Graph of Sine and Cosine Function
Using a Calculator for Trigonometric Values
Calculators can compute trigonometric function values for given angles, typically in degrees or radians. Ensuring the calculator is set to the correct mode (degrees for this problem) is essential for accurate results.
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4:45How to Use a Calculator for Trig Functions
Rounding to Four Decimal Places
After calculating the sine value, the result should be rounded to four decimal places. This means keeping four digits after the decimal point and rounding the last digit based on the fifth digit to maintain precision.
Recommended video:
1:37Example 1
Related Practice
Textbook Question
In Exercises 37–38, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ, or state that the function is undefined.
(0, -1)
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Textbook Question
In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.
tan θ > 0 and sec θ > 0
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Textbook Question
Find a cofunction with the same value as the given expression.
cos (3𝜋/8)
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Textbook Question
In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places.
-4.8 radians
Textbook Question
In Exercises 35–60, find the reference angle for each angle.
355°
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