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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Capitolo 1, Problema 43
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
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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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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Percorso guidato
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 2π radians. Angles can be expressed in radians without converting to degrees, which simplifies calculations involving the unit circle.
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Percorso guidato
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.
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Percorso guidato
6:36Quadratic Formula
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Find the reference angle for each angle.
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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 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 44–48, find the reference angle for each angle.
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