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 6

Chapter 1, Problem 6

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

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Recall the definitions of angle classifications in radians: an acute angle is between 0 and \( \frac{\pi}{2} \) radians, a right angle is exactly \( \frac{\pi}{2} \) radians, an obtuse angle is between \( \frac{\pi}{2} \) and \( \pi \) radians, and a straight angle is exactly \( \pi \) radians.

Identify the given angle measure, which is \( \frac{\pi}{2} \) radians.

Compare the given angle \( \frac{\pi}{2} \) to the classifications: since it matches exactly \( \frac{\pi}{2} \), it fits the definition of a right angle.

Conclude that the angle \( \frac{\pi}{2} \) is classified as a right angle.

Remember that this classification is based on the radian measure and the standard angle definitions.

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Key Concepts

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

Radian Measure of Angles

Radian is a unit for measuring angles based on the radius of a circle. One radian is the angle subtended by an arc equal in length to the radius. Understanding radians allows conversion between radians and degrees, which is essential for classifying angles given in radian measure.

Classification of Angles

Angles are classified by their measure: acute angles are less than 90° (π/2 radians), right angles equal 90° (π/2 radians), obtuse angles are between 90° and 180° (π/2 to π radians), and straight angles equal 180° (π radians). This classification helps identify the type of angle from its measure.

Conversion Between Radians and Degrees

To classify angles given in radians, it is often helpful to convert them to degrees using the formula: degrees = radians × (180/π). This conversion aids in intuitive understanding and comparison with standard angle classifications.

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Converting between Degrees & Radians

Related Practice

Textbook Question

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

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In Exercises 1–8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then find the value of each of the six trigonometric functions of θ.

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Textbook Question

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋. 6 3 2 3 6 6 3 2 3 6 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. sin 𝜋/3

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

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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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