Textbook Question
In Exercises 39β48, use a calculator to find the value of the trigonometric function to four decimal places.
tan 32.7Β°
671
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
Chapter 1, Problem 43
In Exercises 41β56, 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.
3π/4
Verified step by step guidance1
Understand that the angle is given in radians and is in standard position, meaning its vertex is at the origin and the initial side lies along the positive x-axis.
Recall that one full revolution around the circle corresponds to \(2\pi\) radians, and the circle is divided into four quadrants, each spanning \(\frac{\pi}{2}\) radians.
Locate the angle \(\frac{3\pi}{4}\) on the circle by starting from the positive x-axis and moving counterclockwise \(\frac{3\pi}{4}\) radians.
Since \(\frac{3\pi}{4}\) is greater than \(\frac{\pi}{2}\) but less than \(\pi\), the terminal side of the angle lies in the second quadrant.
Draw the angle on the circle by marking the terminal side at \(\frac{3\pi}{4}\) radians, which is halfway between \(\frac{\pi}{2}\) and \(\pi\), and label the quadrant as the second quadrant.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angles in Standard Position
An angle is in standard position when its vertex is at the origin of the coordinate system, and its initial side lies along the positive x-axis. The angle is measured by rotating the terminal side from the initial side, counterclockwise for positive angles and clockwise for negative angles.
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05:50
Drawing Angles in Standard Position
Radian Measure and the Unit Circle
Radian measure relates the length of an arc on the unit circle to the radius. One full revolution around the circle equals 2Ο radians. Angles can be expressed in radians without converting to degrees, which simplifies calculations involving the unit circle.
Recommended video:
06:11Introduction to the Unit Circle
Quadrants of the Coordinate Plane
The coordinate plane is divided into four quadrants, numbered counterclockwise starting from the upper right. The quadrant in which the terminal side of an angle lies determines the sign of the sine and cosine values and helps in identifying the angle's position.
Recommended video:
6:36Quadratic Formula
Related Practice
Textbook Question
Find the reference angle for each angle.
5Ο/4
591
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Textbook Question
In Exercises 33β42, let sin t = a, cos t = b, and tan t = c. Write each expression in terms of a, b, and c.
cos t + cos(t + 1000π) - tan t - tan(t + 999π) - sin t + 4 sin(t - 1000π)
574
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Textbook Question
In Exercises 39β48, use a calculator to find the value of the trigonometric function to four decimal places.
csc 17Β°
702
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Textbook Question
In Exercises 41β56, 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.
7π/4
617
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Textbook Question
In Exercises 44β48, find the reference angle for each angle.
265Β°
726
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