Find the missing coordinate. Round your answers to two decimal places.(x, 5)(6, у)152°65°35°-48(х, у)(х, -3)

Answered: (х, 5) (6, у) 152° 65° 35° 1 (х, у) -48…

Math

Trigonometry

(х, 5) (6, у) 152° 65° 35° 1 (х, у) -48 (х, -3)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 7E

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Question

Find the missing coordinate. Round your answers to two decimal places.
(x, 5)
(6, у)
152°
65°
35°
-48
(х, у)
(х, -3)

Expert Solution

Step 1

Let the points in the diagram be referred as, $A (x, 5), B (- 6, y), C (x, y), D (x, - 3), and O (0, 0)$ .

Also let $θ$ represents the angle made by the position vector with the positive x-axis.

Consider the formula,

$x - c o o r d i n a t e = (l e n g t h o f t h e l i n e) \cdot \cos (θ)$
$y - c o o r d i n a t e = (l e n g t h o f t h e l i n e) \cdot \sin (θ)$

POINT A:

The y-coordinate is 5,

$O A \cdot \sin (65 °) = 5 \Rightarrow O A = 5.517$

Solve for x-coordinate as,

$x = 5.517 \cdot \cos (65 °) \Rightarrow x = 2.33$

Thus, the coordinate of point A is $(2.33, 5)$ .

Step 2

POINT B:

The x-coordinate is given as -6,

$O B \cdot \cos (152 °) = - 6 \Rightarrow O B = 6.795$

Solve for the y-coordinate as,

$y = 6.795 \cdot \sin (152 °) \Rightarrow y = 3.19$

Thus, the coordinate of point B is $(- 6, 3.19)$ .

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