Domanda del libro di testo
In Exercises 44–48, find the reference angle for each angle.
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Capitolo 1, Problema 47
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.
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Guida verificata passo dopo passo1
Identify that the angle given is \(\frac{5\pi}{4}\) radians, which is in standard position, meaning it starts from the positive x-axis and rotates counterclockwise.
Recall that one full rotation around the circle is \(2\pi\) radians, and the circle is divided into four quadrants, each spanning \(\frac{\pi}{2}\) radians.
Calculate the approximate position of \(\frac{5\pi}{4}\) by noting that \(\frac{4\pi}{4} = \pi\) radians corresponds to the negative x-axis, so \(\frac{5\pi}{4}\) is \(\frac{\pi}{4}\) radians past \(\pi\).
Determine that \(\frac{5\pi}{4}\) lies in the third quadrant because it is between \(\pi\) and \(\frac{3\pi}{2}\) radians.
To draw the angle, start from the positive x-axis, rotate counterclockwise past \(\pi\) (180 degrees), and continue \(\frac{\pi}{4}\) radians (45 degrees) into the third quadrant.
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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 terminal side is determined by rotating the initial side counterclockwise for positive angles and clockwise for negative angles.
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Percorso guidato
05:50
Drawing Angles in Standard Position
Radian Measure and Circle Division
Radian measure relates the length of an arc on a unit circle to the angle it subtends. One full rotation around the circle equals 2π radians. The circle is divided into quadrants, each spanning π/2 radians, which helps locate the angle's terminal side.
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5:04Converting between Degrees & Radians
Quadrants in the Coordinate Plane
The coordinate plane is divided into four quadrants: I (x>0, y>0), II (x<0, y>0), III (x<0, y<0), and IV (x>0, y<0). The quadrant in which an angle's terminal side lies is determined by the angle's radian measure and helps in understanding the sign of trigonometric functions.
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Percorso guidato
6:36Quadratic Formula
Pratica correlata
Domanda del libro di testo
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.
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Domanda del libro di testo
In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
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Domanda del libro di testo
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.
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Domanda del libro di testo
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.
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Domanda del libro di testo
In Exercises 44–48, find the reference angle for each angle.
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