Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

1. Measuring Angles

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

Previous problemNext problem

1:52 minutes

Problem 55

Textbook Question

In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree.sin θ = 0.2974

Verified step by step guidance

Identify the trigonometric function given in the problem, which is \( \sin \theta = 0.2974 \).

To find the angle \( \theta \), use the inverse sine function, denoted as \( \sin^{-1} \) or \( \arcsin \).

Input the value 0.2974 into your calculator and apply the inverse sine function: \( \theta = \sin^{-1}(0.2974) \).

Ensure your calculator is set to degree mode, as the problem asks for the angle in degrees.

Round the result to the nearest degree to find the value of the acute angle \( \theta \).

Verified video answer for a similar problem:

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

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arcsin, arccos, and arctan, are used to find angles when the values of the trigonometric ratios are known. In this case, since sin θ = 0.2974, we can use the arcsin function to determine the angle θ. This function essentially reverses the sine operation, allowing us to solve for the angle corresponding to a given sine value.

Calculator Functions

Most scientific calculators have built-in functions for calculating inverse trigonometric values. To find θ when sin θ = 0.2974, you would input the value into the arcsin function on the calculator. It's important to ensure that the calculator is set to the correct mode (degrees or radians) based on the requirements of the problem, as this will affect the output angle.

Acute Angles

An acute angle is defined as an angle that measures less than 90 degrees. In the context of trigonometric functions, the sine function is positive in the first quadrant, where all angles are acute. Therefore, when solving for θ in this problem, we are specifically looking for the acute angle that corresponds to the sine value of 0.2974, ensuring that the solution falls within the appropriate range.