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(a) If Q is the point (x, sin 16)), find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (i) 2 (ii) 1.5 1.7320 (iii) 1.4 -1.6249 (iv) 1.3 1.1757 (v) 1.2 -1.0825 (vi) 1.1 1.0998 (vii) 0.5

(a) If Q is the point (x, sin 16)), find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (i) 2 (ii) 1.5 1.7320 (iii) 1.4 -1.6249 (iv) 1.3 1.1757 (v) 1.2 -1.0825 (vi) 1.1 1.0998 (vii) 0.5

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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167 (a) If Q is the point (x, sin find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (i) 2 (ii) 1.5 1.7320 (iii) 1.4 -1.6249 (iv) 1.3 1.1757 (v) 1.2 |-1.0825 (vi) 1.1 1.0998 (vii) 0.5 (viii) 0.6 |0.6186 (ix) 0.7 (x) 0.8 0.3337 (xi) 0.9 |-0.5843 Do the slopes appear to be approaching a limit? As x approaches 1, the slopes approach 1 (b) Use a graph of the curve to explain why the slopes of the secant lines in part (a) are not close to the slope of the tangent line at P. We see that problems with estimation are caused by the discontinuities vx of the graph. The tangent is so steep at P that we need to take x-values --Select--- v to 1 in order to get accurate estimates of its slope. (c) By choosing appropriate secant lines, estimate the slope of the tangent line at P. (Round your answer to two decimal places.)
Transcribed Image Text:167 (a) If Q is the point (x, sin find the slope of the secant line PQ (correct to four decimal places) for the following values of x. (i) 2 (ii) 1.5 1.7320 (iii) 1.4 -1.6249 (iv) 1.3 1.1757 (v) 1.2 |-1.0825 (vi) 1.1 1.0998 (vii) 0.5 (viii) 0.6 |0.6186 (ix) 0.7 (x) 0.8 0.3337 (xi) 0.9 |-0.5843 Do the slopes appear to be approaching a limit? As x approaches 1, the slopes approach 1 (b) Use a graph of the curve to explain why the slopes of the secant lines in part (a) are not close to the slope of the tangent line at P. We see that problems with estimation are caused by the discontinuities vx of the graph. The tangent is so steep at P that we need to take x-values --Select--- v to 1 in order to get accurate estimates of its slope. (c) By choosing appropriate secant lines, estimate the slope of the tangent line at P. (Round your answer to two decimal places.)
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