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

5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Inverse Sine, Cosine, & Tangent

Trigonometry

5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Inverse Sine, Cosine, & Tangent

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Problem 6.59

Textbook Question

Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = arcsin 0.92837781

Verified step by step guidance

Ensure your calculator is set to radian mode, as this is crucial for trigonometric calculations involving angles in radians.

Identify the function you need to use: in this case, it's the inverse sine function, denoted as \( \arcsin \).

Enter the value 0.92837781 into your calculator.

Apply the \( \arcsin \) function to the value entered. This will give you the angle \( y \) in radians.

The calculator will display the approximate value of \( y \), which is the angle whose sine is 0.92837781.

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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, are used to find the angle whose sine is a given number. For example, if y = arcsin(x), then sin(y) = x. These functions are essential for solving problems where the angle is unknown but the sine value is provided.

Radian Measure

Radian measure is a way of measuring angles based on the radius of a circle. One radian is the angle formed when the arc length is equal to the radius. Calculators often have settings for degrees and radians, and it's crucial to ensure the correct mode is selected when performing trigonometric calculations.

Calculator Functions

Using a calculator effectively involves understanding its functions, especially for trigonometric calculations. When calculating arcsin, the calculator must be set to radian mode to provide the correct output in radians. Familiarity with the calculator's interface and functions is vital for accurate computations.