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Trig

Trig. 2.3 Polar Coordinates Objective: to convert rectangular coordinates to polar and vice versa. Review Complex Plane.

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Trig

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  1. Trig 2.3 Polar Coordinates Objective: to convert rectangular coordinates to polar and vice versa

  2. Review Complex Plane Imagine that you are walking to the point 2 + 3i. Instead of walking 2 units right, turning 90⁰, and walking 3 more units, you want to take the nearest route. You need to have a direction and a distance to walk. What is the direction you need to take? How far should you walk?

  3. Polar Coordinates Every polar coordinate has both an angle (direction) and a radius (distance). (r, θ) Partner Work – each group needs a balloon, two rubber bands, and a permanent marker. One person will be the coach, the other is the recorder.

  4. Plot the Points • (4, 0⁰) • (2, 3π/2) • (-2, 210⁰) • (3, 135⁰) • Now, on paper, plot the following points: • (4, 30o) • (-4, 225o) • (2, -300o) • (-3, -270o)

  5. Polar Form of Complex Numbers • The polar form or trigonometric form of the complex number a + bi is r(cosθ + i sin θ). • To express -3 + 4i in polar form, first find the radius and the argument. • r = √(32 + 42) θ = tan-1(4/-3) QII • -3 + 4i = 5(cos 2.21 + i sin 2.21) = 5 cis 2.21 • Express 2 – 2i√5 in polar form. • Express 1 + √3i in polar form.

  6. From Polar Form to Rectangular • a = r cosθand b = r sin θ • Express 5 cisπ/6 in rectangular form. • x = 5 cos 30⁰ y = 5 sin 30⁰ • x = 5 (√(3)/2) y = 5 (1/2) • 5√3/2 + 5/2 i • Express 10 cis 300⁰ in rectangular form. • Express 4 cis 135o in rectangular form.

  7. Practice Problems • Find the magnitude and argument of each of the following numbers. 2√3 – 2i 4 cis 300o • If z = 5 cis 75o and w = 2 cis 100o, find |zw| and arg(zw). • Assignment page 95 8, 9a, 10, 15

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