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 41
In Exercises 35–60, find the reference angle for each angle.
7𝜋/4
Guida verificata passo dopo passo1
Identify the given angle: \(\frac{7\pi}{4}\) radians.
Recall that the reference angle is the acute angle formed between the terminal side of the given angle and the x-axis.
Determine the quadrant in which \(\frac{7\pi}{4}\) lies. Since \(\pi\) is \(4\pi/4\), and \(2\pi\) is \(8\pi/4\), \(\frac{7\pi}{4}\) is between \(\frac{3\pi}{2}\) (\(6\pi/4\)) and \(2\pi\) (\(8\pi/4\)), so it lies in the fourth quadrant.
For angles in the fourth quadrant, the reference angle \(\theta_{ref}\) is calculated as \(\theta_{ref} = 2\pi - \theta\). Substitute \(\theta = \frac{7\pi}{4}\) to get \(\theta_{ref} = 2\pi - \frac{7\pi}{4}\).
Simplify the expression for the reference angle to find its value in radians.
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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 any angle to an acute angle.
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Percorso guidato
5:31
Reference Angles on the Unit Circle
Radians and Angle Measurement
Angles can be measured in radians, where 2𝜋 radians equal 360°. Understanding how to convert and interpret angles in radians is essential for finding reference angles, especially when the given angle exceeds 2𝜋 or is expressed as a fraction of 𝜋.
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Percorso guidato
5:04Converting between Degrees & Radians
Quadrants and Angle Positioning
The coordinate plane is divided into four quadrants, each affecting the sign and calculation of reference angles. Knowing which quadrant an angle lies in helps determine how to calculate its reference angle by measuring the distance to the nearest x-axis.
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Percorso guidato
05:50Drawing Angles in Standard Position
Pratica correlata
Domanda del libro di testo
In Exercises 41–43, find the exact value of each of the remaining trigonometric functions of θ.
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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.
cos t + cos(t + 1000𝜋) - tan t - tan(t + 999𝜋) - sin t + 4 sin(t - 1000𝜋)
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Domanda del libro di testo
In Exercises 35–40, convert each angle in radians to degrees. Round to two 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 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.
tan θ > 0 and cos θ < 0
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