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Ch. 5 - Complex Numbers, Polar Coordinates and Parametric Equations
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 3rd EditionCh. 5 - Complex Numbers, Polar Coordinates and Parametric Equations문제 39
5장, 문제 39

In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point. (7.4, 2.5)

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1
Recall the relationship between polar coordinates \((r, \theta)\) and rectangular coordinates \((x, y)\), where \(x = r \cos(\theta)\) and \(y = r \sin(\theta)\).
Identify the given polar coordinates: \(r = 7.4\) and \(\theta = 2.5\) radians.
Calculate the \(x\)-coordinate using the formula \(x = 7.4 \times \cos(2.5)\).
Calculate the \(y\)-coordinate using the formula \(y = 7.4 \times \sin(2.5)\).
Express the rectangular coordinates as the ordered pair \((x, y)\) using the values found in the previous steps.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 given point (7.4, 2.5) means r = 7.4 and θ = 2.5 radians.
추천 영상:
05:32
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.
추천 영상:
06:17
Convert Points from Polar to Rectangular

Trigonometric Functions (Sine and Cosine)

Sine and cosine functions relate an angle in a right triangle to the ratios of its sides. Cosine gives the ratio of the adjacent side to the hypotenuse, and sine gives the ratio of the opposite side to the hypotenuse, essential for coordinate conversion.
추천 영상:
5:53
Graph of Sine and Cosine Function
관련 실천
교과서 질문

In Exercises 21–40, eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that −∞ < t < ∞. x = 2ᵗ, y = 2⁻ᵗ; t ≥ 0

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In Exercises 35–44, test for symmetry and then graph each polar equation. r = 1 / 1−cos θ

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교과서 질문

In Exercises 33–40, polar coordinates of a point are given. Find the rectangular coordinates of each point. (−4, π/2)

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In Exercises 37–52, perform the indicated operations and write the result in standard form. ___ ___ 5√−16 + 3√−81

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In Exercises 37–52, perform the indicated operations and write the result in standard form. ___ ___ √−64 − √−25

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교과서 질문

In Exercises 37–44, find the product of the complex numbers. Leave answers in polar form. z₁ = 6(cos 20° + i sin 20°) z₂ = 5(cos 50° + i sin 50°)

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