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24 The terminal side of an angle 0 in standard position intersects the unit circle at 25 25 What is tan (0)? Write your answer in simplified, rationalized form. /3

24 The terminal side of an angle 0 in standard position intersects the unit circle at 25 25 What is tan (0)? Write your answer in simplified, rationalized form. /3

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Problem Statement The terminal side of an angle θ in standard position intersects the unit circle at \( \left(\frac{7}{25}, \frac{24}{25}\right) \). #### Question What is \( \tan(\theta) \)? *Write your answer in simplified, rationalized form.* ### Input Area Below the question, there is an input field where students can type their answers. The input field is accompanied by a button with a fraction and a square root symbol, likely for inputting complex and precise mathematical expressions. ### Submit Button Once the student has entered their answer, they can click the "Submit" button, which is green and located below the input area. This likely submits their answer for grading or further feedback. ### Educational Context When analyzing the coordinates of a point on the unit circle, the tangent of the angle θ can be found using the ratio of the y-coordinate to the x-coordinate (i.e., \( \tan(\theta) = \frac{y}{x} \)). In this problem: - x-coordinate = \( \frac{7}{25} \) - y-coordinate = \( \frac{24}{25} \) Therefore, \( \tan(\theta) = \frac{\frac{24}{25}}{\frac{7}{25}} = \frac{24}{25} \times \frac{25}{7} = \frac{24}{7} \). Hence, the value of \( \tan(\theta) \) is \( \frac{24}{7} \), and this is already in its simplest form. This problem assists students in understanding trigonometric relationships on the unit circle and enhances their ability to simplify and rationalize fractions.
Transcribed Image Text:### Problem Statement The terminal side of an angle θ in standard position intersects the unit circle at \( \left(\frac{7}{25}, \frac{24}{25}\right) \). #### Question What is \( \tan(\theta) \)? *Write your answer in simplified, rationalized form.* ### Input Area Below the question, there is an input field where students can type their answers. The input field is accompanied by a button with a fraction and a square root symbol, likely for inputting complex and precise mathematical expressions. ### Submit Button Once the student has entered their answer, they can click the "Submit" button, which is green and located below the input area. This likely submits their answer for grading or further feedback. ### Educational Context When analyzing the coordinates of a point on the unit circle, the tangent of the angle θ can be found using the ratio of the y-coordinate to the x-coordinate (i.e., \( \tan(\theta) = \frac{y}{x} \)). In this problem: - x-coordinate = \( \frac{7}{25} \) - y-coordinate = \( \frac{24}{25} \) Therefore, \( \tan(\theta) = \frac{\frac{24}{25}}{\frac{7}{25}} = \frac{24}{25} \times \frac{25}{7} = \frac{24}{7} \). Hence, the value of \( \tan(\theta) \) is \( \frac{24}{7} \), and this is already in its simplest form. This problem assists students in understanding trigonometric relationships on the unit circle and enhances their ability to simplify and rationalize fractions.
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