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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 22c
Capitolo 9, Problema 22c

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


(4 , 3π/2)

Guida verificata passo dopo passo
1
Recall the relationship between polar coordinates \((r, \theta)\) and rectangular coordinates \((x, y)\), which is given by the formulas: \(x = r \cos(\theta)\) and \(y = r \sin(\theta)\).
Identify the given polar coordinates: \(r = 4\) and \(\theta = \frac{3\pi}{2}\).
Calculate the \(x\)-coordinate using the formula: \(x = 4 \times \cos\left(\frac{3\pi}{2}\right)\).
Calculate the \(y\)-coordinate using the formula: \(y = 4 \times \sin\left(\frac{3\pi}{2}\right)\).
Combine the results from steps 3 and 4 to write the rectangular coordinates as \((x, y)\).

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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 pair (r, θ) specifies the location uniquely, where r ≥ 0 and θ is usually in 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-angle format 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 values for standard angles, especially multiples of π/2, is essential. For example, cos(3π/2) = 0 and sin(3π/2) = -1, which helps in accurately computing the rectangular coordinates.
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Introduction to Trigonometric Functions
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