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

Verified step by step guidance

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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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.

Recommended video:

5:04

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

1042

views

Textbook Question

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

557

views

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

789

views

Textbook Question

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

537

views

Textbook Question

In Exercises 5–7, convert each angle in radians to degrees. 5𝜋 3

590

views

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)

509

views