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27. The perpendicular distance ON from the origin t line L is p, and ON makes an angle a with the positiv x-axis. Show that L has equation How x cos a + y sin a = p.

27. The perpendicular distance ON from the origin t line L is p, and ON makes an angle a with the positiv x-axis. Show that L has equation How x cos a + y sin a = p.

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 94E
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Given that the F vs. C graph is a straight line, find its equation from the following data: (C = 0, 212) are coordinates of F = 32) and (C = 100, F two points on the graph. (b) Is there a temperature at which C = F? If so, what is it? 27. The perpendicular distance ON from the origin to line L is p, and ON makes an angle a with the positive x-axis. Show that L has equation H.W x cos a + y sin a = p. 28. In connection with Problem 2 and Eq. (10), explain the rule: If Arı + By₁ + C agrees in sign with B, then the point P₁(x1, y1) is above L; if the sign is opposite to the sign of B, then the point is below L. (Assume that B0. If B 0, the line is parallel
Transcribed Image Text:Given that the F vs. C graph is a straight line, find its equation from the following data: (C = 0, 212) are coordinates of F = 32) and (C = 100, F two points on the graph. (b) Is there a temperature at which C = F? If so, what is it? 27. The perpendicular distance ON from the origin to line L is p, and ON makes an angle a with the positive x-axis. Show that L has equation H.W x cos a + y sin a = p. 28. In connection with Problem 2 and Eq. (10), explain the rule: If Arı + By₁ + C agrees in sign with B, then the point P₁(x1, y1) is above L; if the sign is opposite to the sign of B, then the point is below L. (Assume that B0. If B 0, the line is parallel
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