Textbook Question
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.
sin(-t - 2𝜋) - cos(-t - 4𝜋) - tan(-t - 𝜋)
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
Chapter 1, Problem 39
In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places.
-4.8 radians
Verified step by step guidance1
Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).
Substitute the given radian measure into the formula: \(\text{degrees} = -4.8 \times \frac{180}{\pi}\).
Calculate the fraction \(\frac{180}{\pi}\) to get the approximate degree equivalent of one radian.
Multiply the radian value by the calculated fraction to find the angle in degrees.
Round the resulting degree value to two decimal places as required.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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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5:04
Converting between Degrees & Radians
Conversion Between Radians and Degrees
To convert radians to degrees, multiply the radian value by 180/π. This ratio comes from the fact that 2π radians equal 360 degrees, so 1 radian equals approximately 57.2958 degrees.
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5:04Converting between Degrees & Radians
Rounding Decimal Values
Rounding involves limiting a number to a specified number of decimal places for simplicity and clarity. In this case, the converted degree value should be rounded to two decimal places, ensuring precision without unnecessary detail.
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5:08Sine, Cosine, & Tangent of 30°, 45°, & 60°
Related Practice
Textbook Question
In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies.
tan θ > 0 and sec θ > 0
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Textbook Question
Find a cofunction with the same value as the given expression.
cos (3𝜋/8)
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Textbook Question
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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Textbook Question
In Exercises 35–60, find the reference angle for each angle.
355°
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Textbook Question
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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