Domanda del libro di testo
In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
tan 32.7°
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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TOC.tableOfContents
Capitolo 1, Problema 42
Find the reference angle for each angle.
5π/4
Guida verificata passo dopo passo1
Understand that the reference angle is the acute angle formed between the terminal side of the given angle and the x-axis.
Since the angle is given in radians, recall that one full rotation is \(2\pi\) radians, and the quadrants are divided as follows: Quadrant I: \(0\) to \(\frac{\pi}{2}\), Quadrant II: \(\frac{\pi}{2}\) to \(\pi\), Quadrant III: \(\pi\) to \(\frac{3\pi}{2}\), Quadrant IV: \(\frac{3\pi}{2}\) to \(2\pi\).
Determine which quadrant the angle \(\frac{5\pi}{4}\) lies in by comparing it to these boundaries.
For an angle in Quadrant III, the reference angle \(\theta_{ref}\) is found by subtracting \(\pi\) from the given angle: \(\theta_{ref} = \theta - \pi\).
Apply this formula to find the reference angle for \(\frac{5\pi}{4}\) by calculating \(\frac{5\pi}{4} - \pi\).
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Reference Angle
A reference angle is the acute angle formed between the terminal side of a given angle and the x-axis. It is always positive and less than or equal to 90°, used to simplify trigonometric calculations by relating angles in different quadrants to their acute counterparts.
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Percorso guidato
5:31
Reference Angles on the Unit Circle
Radians and the Unit Circle
Angles can be measured in radians, where 2π radians equal 360°. The unit circle helps visualize angles and their positions in different quadrants, which is essential for determining reference angles and understanding trigonometric function values.
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Percorso guidato
06:11Introduction to the Unit Circle
Quadrants and Angle Positioning
The coordinate plane is divided into four quadrants, each affecting the sign and calculation of trigonometric functions. Knowing which quadrant an angle lies in helps determine how to find its reference angle by measuring the shortest distance to the x-axis.
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Percorso guidato
05:50Drawing Angles in Standard Position
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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 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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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 44–48, find the reference angle for each angle.
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