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Warm-Up 12/05Identify all angles that are coterminal with the given angle. Then give one positive and one negative angle coterminal with the given angle.
1. 165° 2. 165° + 360k°525°; – 195°
+ 2k°
;
Rigor:You will learn how graph points and simple
graphs with polar coordinates.
Relevance:You will be able to use Polar Coordinates to solve
real world problems.
Polar Coordinate System or polar planePole is the origin Polar axis is an initial ray from the pole.Polar Coordinates (r, ) r is directed distance from the pole is the directed angle from the polar axis.
In a rectangular coordinate system each point has a unique set of coordinate. This is not true in a polar coordinate system.
Example 3: Find four different pairs of polar coordinates that name point T if – 360°≤ ≤ 360°.
(4, 135°)
(4, 135°) = (4, 135° – 360°) = (4, – 225°)
(4, 135°) = (– 4, 135° + 180°)
(4, 135°) = (– 4, 135° – 180°)= (–4, 315°)= (–4, – 45°)
Polar equation is an equation expressed in terms of polar coordinates. For example, r = 2 sin.
Polar graph is the set of all points with coordinates (r, ) that satisfy a given polar equation.
Example 5: Find the distance between the pair of points.
A(5, 310°), B(6, 345°)
𝐴𝐵=√𝑟12+𝑟 2
2−2𝑟1𝑟2 cos (𝜃2−𝜃1 )
𝐴𝐵=√52+62−2 (5 ) (6 )cos (345 °−310 ° )
𝐴𝐵≈3.4425