Textbook Question
In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
csc 17°
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1. Measuring Angles
Angles in Standard Position
1:37 minutesProblem 1.2.57
Textbook Question
In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. tan θ = 4.6252
Verified step by step guidance1
Identify that the problem requires finding the acute angle \( \theta \) such that \( \tan \theta = 4.6252 \). Since \( \theta \) is acute, it lies between 0° and 90°.
Recall that to find an angle from its tangent value, you use the inverse tangent function (also called arctangent), denoted as \( \tan^{-1} \) or \( \arctan \).
Set up the equation \( \theta = \tan^{-1}(4.6252) \) to find the angle \( \theta \).
Use a calculator in degree mode to evaluate \( \tan^{-1}(4.6252) \). Make sure your calculator is set to degrees, not radians.
Round the resulting angle to the nearest whole degree to get the value of the acute angle \( \theta \).
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Tangent Function
The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the adjacent side. It is a fundamental trigonometric function used to relate angles to side lengths. Understanding tan θ helps in finding the angle when the ratio is known.
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Introduction to Tangent Graph
Inverse Tangent (Arctan) Function
The inverse tangent function, denoted as arctan or tan⁻¹, is used to find the angle whose tangent is a given number. It allows us to determine the angle θ when tan θ is known, which is essential for solving the problem using a calculator.
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Using a Calculator for Trigonometric Functions
Calculators can compute inverse trigonometric functions to find angles from ratios. It is important to ensure the calculator is set to the correct mode (degrees or radians) and to round the result appropriately, as the question asks for the angle to the nearest degree.
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