Domanda del libro di testo
In Exercises 35–60, find the reference angle for each angle.
7𝜋/4
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Capitolo 1, Problema 40
In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places.
-5.2 radians
Guida verificata passo dopo passo1
Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).
Substitute the given radian measure into the formula: \(\text{degrees} = -5.2 \times \frac{180}{\pi}\).
Calculate the fraction \(\frac{180}{\pi}\) to get the approximate degree equivalent of one radian.
Multiply the radian value by the approximate degree equivalent to find the angle in degrees.
Round the resulting degree value to two decimal places as required.
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Radian Measure
A radian is a unit of angular measure based on the radius of a circle. One radian is the angle created when the arc length equals the radius. It is a standard unit in trigonometry, where 2π radians equal 360 degrees.
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Percorso guidato
5:04
Converting between Degrees & Radians
Degree Measure
Degrees are another unit for measuring angles, where a full circle is divided into 360 equal parts. Degrees are often used in practical applications and are related to radians through a fixed conversion factor.
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Percorso guidato
5:04Converting between Degrees & Radians
Conversion Between Radians and Degrees
To convert radians to degrees, multiply the radian value by 180/π. This conversion uses the fact that 2π radians equal 360 degrees. After conversion, rounding to the desired decimal places ensures precision.
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5:04Converting between Degrees & Radians
Pratica correlata
Domanda del libro di testo
In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places.
-4.8 radians
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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.
sin 38°
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Domanda del libro di testo
In Exercises 41–43, find the exact value of each of the remaining trigonometric functions of θ.
cos θ = 2/5, sin θ < 0
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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.
7𝜋/6
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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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