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Use the figures to evaluate the function if f(x) = tan x. f(a+ B) (x,-1) f(a + B) = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

Use the figures to evaluate the function if f(x) = tan x. f(a+ B) (x,-1) f(a + B) = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

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:** Use the figures to evaluate the function if \( f(x) = \tan x \). Evaluate \( f(\alpha + \beta) \). (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) **Diagrams Explanation:** 1. **First Diagram**: - Represents a circle with the equation \( x^2 + y^2 = 4 \). - An angle \( \alpha \) is shown in standard position, with its terminal side intersecting the circle. - The intersection point on the circle is labeled as \( (x, -1) \). 2. **Second Diagram**: - Represents a circle with the equation \( x^2 + y^2 = 1 \). - An angle \( \beta \) is shown in standard position, with its terminal side intersecting the circle. - The intersection point on the circle is labeled as \( \left( \frac{1}{3}, y \right) \). **Objective:** Calculate the exact value of \( f(\alpha + \beta) \) using the given information from both diagrams.
Transcribed Image Text:**Problem Statement:** Use the figures to evaluate the function if \( f(x) = \tan x \). Evaluate \( f(\alpha + \beta) \). (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) **Diagrams Explanation:** 1. **First Diagram**: - Represents a circle with the equation \( x^2 + y^2 = 4 \). - An angle \( \alpha \) is shown in standard position, with its terminal side intersecting the circle. - The intersection point on the circle is labeled as \( (x, -1) \). 2. **Second Diagram**: - Represents a circle with the equation \( x^2 + y^2 = 1 \). - An angle \( \beta \) is shown in standard position, with its terminal side intersecting the circle. - The intersection point on the circle is labeled as \( \left( \frac{1}{3}, y \right) \). **Objective:** Calculate the exact value of \( f(\alpha + \beta) \) using the given information from both diagrams.
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