Textbook Question
Work each problem.
Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?
3
Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 4, Problem 2d
Work each problem.
Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?
7
Verified step by step guidance1
Recall that the quadrants in the coordinate plane are divided by the angles: Quadrant I (0 to \( \frac{\pi}{2} \)), Quadrant II (\( \frac{\pi}{2} \) to \( \pi \)), Quadrant III (\( \pi \) to \( \frac{3\pi}{2} \)), and Quadrant IV (\( \frac{3\pi}{2} \) to \( 2\pi \)).
Since the angle given is in radians, first find the equivalent angle between 0 and \( 2\pi \) by subtracting multiples of \( 2\pi \) from 7 until the result lies within this range.
Calculate \( 7 - 2\pi \) to find the coterminal angle between 0 and \( 2\pi \).
Determine which quadrant this coterminal angle lies in by comparing it to the quadrant boundaries: 0 to \( \frac{\pi}{2} \), \( \frac{\pi}{2} \) to \( \pi \), \( \pi \) to \( \frac{3\pi}{2} \), or \( \frac{3\pi}{2} \) to \( 2\pi \).
Conclude the quadrant where the terminal side of the angle lies based on the coterminal angle's position.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Standard Position of an Angle
An angle in standard position has its vertex at the origin and its initial side along the positive x-axis. The terminal side is determined by rotating the initial side counterclockwise for positive angles or clockwise for negative angles. Understanding this helps locate the angle's terminal side on the coordinate plane.
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Drawing Angles in Standard Position
Radian Measure and Its Relation to Quadrants
Radian measure quantifies angles based on the radius of a circle, where 2π radians equal 360 degrees. The unit circle is divided into four quadrants, each spanning π/2 radians. Knowing how to convert or compare radian values to these quadrant boundaries is essential to identify the terminal side's quadrant.
Recommended video:
5:04Converting between Degrees & Radians
Quadrants of the Coordinate Plane
The coordinate plane is divided into four quadrants: Quadrant I (0 to π/2), Quadrant II (π/2 to π), Quadrant III (π to 3π/2), and Quadrant IV (3π/2 to 2π). Determining which quadrant an angle's terminal side lies in requires comparing the angle's radian measure to these intervals.
Recommended video:
6:36Quadratic Formula
Related Practice
Textbook Question
The propeller of a 90-horsepower outboard motor at full throttle rotates at exactly 5000 revolutions per min. Find the angular speed of the propeller in radians per second.
Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
cot s = 0.5022
Textbook Question
Find the exact value of s in the given interval that has the given circular function value.
[ π , 3π/2] ; sec s = ―2√3/3
Textbook Question
Work each problem.
Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?
4
Textbook Question
Work each problem.
Consider each angle in standard position having the given radian measure. In what quadrant does the terminal side lie?
-2