Ch. 2 - Acute Angles and Right Triangles

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. 2 - Acute Angles and Right Triangles

Problem 8

Chapter 3, Problem 8

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II.
Column I: 1.
tan⁻¹ 30
Column II:
A. 88.09084757°
B. 63.25631605°
C. 1.909152433°
D. 17.45760312°
E. 0.2867453858
F. 1.962610506
G. 14.47751219°
H. 1.015426612
I. 1.051462224
J. 0.9925461516

Verified step by step guidance

Identify the expressions given in Column I that involve inverse trigonometric functions, such as \( \tan^{-1} 30 \). Recognize that \( \tan^{-1} x \) means the angle whose tangent is \( x \).

Calculate or recall the approximate values of the inverse trigonometric functions in Column I. For example, \( \tan^{-1} 30 \) is the angle whose tangent is 30, which is a relatively large angle in degrees.

Convert the inverse trigonometric values from radians to degrees if necessary, using the conversion formula: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\)

Match each calculated angle or function value from Column I with the closest numerical approximation in Column II by comparing the decimal values or degree measures.

Verify the matches by checking the consistency of the values, ensuring that angles correspond to inverse trig function outputs and numerical values correspond to function values.

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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 tan⁻¹ (arctan), are used to find the angle whose trigonometric ratio is given. For example, tan⁻¹(30) gives the angle whose tangent is 30. Understanding how to compute and interpret these functions is essential for matching angles to their values.

Angle Measurement in Degrees and Radians

Angles can be measured in degrees or radians, and it is important to recognize which unit is being used. Most inverse trig function outputs can be converted between these units. Being comfortable with these conversions helps in accurately matching angles to their decimal approximations.

Approximation and Rounding of Trigonometric Values

Trigonometric values and angles often require approximation to a certain number of decimal places. Understanding how to interpret and compare these approximations is crucial when matching given values to their corresponding angles or function outputs.

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