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Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 8 - Complex Numbers, Polar Equations, and Parametric EquationsProblema 17c
Capitolo 9, Problema 17c

For each pair of polar coordinates, (c) give the rectangular coordinates for the point. See Examples 1 and 2(a).


(5 , ―60°)

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1
Recall that to convert from polar coordinates \((r, \theta)\) to rectangular coordinates \((x, y)\), we use the formulas: \(x = r \cos(\theta)\) \(y = r \sin(\theta)\).
Identify the given polar coordinates: here, \(r = 5\) and \(\theta = -60^\circ\).
Substitute the values into the formulas: \(x = 5 \cos(-60^\circ)\) \(y = 5 \sin(-60^\circ)\).
Use the fact that cosine is an even function and sine is an odd function, so \(\cos(-60^\circ) = \cos(60^\circ)\) \(\sin(-60^\circ) = -\sin(60^\circ)\).
Evaluate the trigonometric values \(\cos(60^\circ)\) and \(\sin(60^\circ)\) using known exact values or a unit circle, then multiply by 5 to find \(x\) and \(y\).

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Polar Coordinates

Polar coordinates represent a point in the plane using a distance from the origin (radius r) and an angle θ measured from the positive x-axis. The point is expressed as (r, θ), where r ≥ 0 and θ is typically in degrees or radians.
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Intro to Polar Coordinates

Conversion from Polar to Rectangular Coordinates

To convert polar coordinates (r, θ) to rectangular coordinates (x, y), use the formulas x = r cos θ and y = r sin θ. This translates the point from a radius and angle to Cartesian coordinates on the xy-plane.
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Convert Points from Polar to Rectangular

Trigonometric Functions and Angle Measurement

Understanding sine and cosine functions and how they relate to angles is essential. Angles can be negative or positive, and the trigonometric values determine the sign and position of the point in the rectangular coordinate system.
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Introduction to Trigonometric Functions
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