Ch. 1 - Angles and the Trigonometric Functions

Blitzer3rd EditionTrigonometryISBN: 9780137316601Not the one you use?Change textbook

Blitzer 3rd Edition

Ch. 1 - Angles and the Trigonometric Functions

Problem 7

Chapter 1, Problem 7

In Exercises 5–7, convert each angle in radians to degrees. - 5𝜋 6

Verified step by step guidance

Recall the conversion formula from radians to degrees: \(\text{Degrees} = \text{Radians} \times \dfrac{180}{\pi}\).

Identify the given angle in radians: \(\dfrac{5\pi}{6}\).

Substitute the given angle into the conversion formula: \(\dfrac{5\pi}{6} \times \dfrac{180}{\pi}\).

Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\dfrac{5}{6} \times 180\).

Multiply the remaining numbers to find the angle in degrees: \(5 \times \dfrac{180}{6}\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Radian Measure

Radian is a unit of angular measure based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. It provides a natural way to measure angles in terms of the circle's geometry.

Degree Measure

Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Each degree represents 1/360 of a full rotation, making it intuitive for everyday use and practical applications.

Conversion between Radians and Degrees

To convert radians to degrees, multiply the radian value by 180/π. This conversion factor arises because π radians equal 180 degrees. For example, converting 5π/6 radians involves multiplying by 180/π to find the equivalent degree measure.

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Converting between Degrees & Radians

Related Practice

Textbook Question

In Exercises 7–12, find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Radius, r: 10 inches Arc Length, s: 40 inches

Textbook Question

In Exercises 8–12, draw each angle in standard position. 5𝜋 6

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Textbook Question

The unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋/6, 𝜋/3, 𝜋/2, 2𝜋/3, 5𝜋/6, 𝜋, 7𝜋/6, 4𝜋/3, 3𝜋/2, 5𝜋/3, 11𝜋/6, and 2𝜋

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.

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cos 5𝜋/6

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Textbook Question

In Exercises 5–7, convert each angle in radians to degrees. 7𝜋 5

Textbook Question

In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 𝜋/2

Textbook Question

In Exercises 1–8, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ. (5, -5)

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