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 6.61

Textbook Question

Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.)
y = cos⁻¹ (―0.32647891)

Verified step by step guidance

Ensure your calculator is in radian mode. This is crucial because the problem specifies that the calculation should be done in radians.

Identify the function you need to use: \( y = \cos^{-1}(-0.32647891) \). This is the inverse cosine function, which will give you the angle whose cosine is \(-0.32647891\).

Enter the value \(-0.32647891\) into your calculator using the inverse cosine function. This is often labeled as \( \cos^{-1} \) or \( \text{acos} \) on calculators.

The calculator will output an angle in radians. This is the value of \( y \).

Interpret the result: The range of the inverse cosine function is from 0 to \( \pi \) radians, so the result will be within this interval.

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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 cos⁻¹ (arccosine), are used to find the angle whose cosine is a given value. These functions are essential for solving problems where the angle is unknown, and they return values within specific ranges, typically between 0 and π for arccosine.

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. Understanding radian measure is crucial when using calculators, as many trigonometric functions are often computed in radians rather than degrees.

Calculator Settings

Using a calculator in the correct mode (radian or degree) is vital for accurate trigonometric calculations. When solving problems involving inverse trigonometric functions, ensuring the calculator is set to radian mode will yield the correct angle in radians, which is necessary for further calculations or applications.