4. Sketch the polar curve r = sinº 0. 90° 135° 45° 180° 0° 225° 315°...
4. Sketch the polar curve r = sin? 0. 90° 135° 45° 180° 0° 225° 315° 270°
[12] Sketch the graph of r = 1.5 + 3sin in the polar plane provided. o 90° 0° 180° 30° 150° 270° 45° 135° 60° 1200 210° 225° 240° 330° 315º 300° r Approximations 12 1.5 + 3 3.6 1.5 - 3 2 2 *-0.6 2 1.5 + 3 13 2 > 4.1 1.5 - 3 sch 3 2 % -1.1 119/12 1/2 511/12 2013 al3 37/4 51/6 11/25 77/2 71 0
[12] Sketch the graph of r = 1.5 + 3sine in the polar plane provided. o 90° 0° 180° 30° 150° 45° 135° 60° 120° 210° 330° 225° 240° 270° 315º 300° 1 Approximations 1.5 + 3 V2 2 3.6 1.5 - 3 2 2 *-0.6 1.5 + 3 13 2 4.1 1.5 - 30 13 % -1.1 2 11/12 1/2 511/12 2013 1/3 3014 9/4 51/6 →% 196/25 7/12 >O
10. Sketch the graph of the polar equation. r=3 90° 4 120° 60° الا 150° 2 30° 180° 0° 210° 330° 240 300° 270°
11. Sketch the graph of the polar equation by plotting points. Complete the table. r = 4 sin e o 0° 30° 45° 60° 75° 90° 1050 1200 135° 150° 1800
The electric current in a given circuit is 4+4 3i amperes (A). The resistance is given by 1+i ohms (Q). Express each of these in polar form. a) The voltage in the circuit is the product of these two. Express the voltage in polar form. Plot all three on the given polar plot. 90" 105* 75 120 60* 135 45 150 30 165 15 180 195 345 210 330 225 315 240 300 255 285 270
Find the resultant vector in both polar and rectangular coordinates. Likewise, sketch it. Refer to the vectors 2 cm, 45° cm,90 . C (2 cm, 180°) . D (2 cm, 270°) . E (2 cm, 60°) . E (2 cm, 0) R-2(E-F) -8 64 -2 -4 Polar Coordinates: Rectangular Coordinates: R=2D + A -8 -64 2 -8 Polar Coordinates: Rectangular Coordinates:
Find the resultant vector in both polar and rectangular coordinates. Likewise, sketch it. Refer to the vectors . A (2 cm,45) . B (2 cm, 90) e C (2 cm, 180) . D (2 cm, 270) . E (2 cm, 60) . F (2 cm,0) R 2D + A -8 6 4 2 Polar Coordinates: Rectangular Coordinates R 2(E F) 64 -2 Polar Coordinates: Rectangular Coordinates: Extra Credit R 3(A -2(D+B) +F) + 2C-3B -8 -6 42 -6 Polar Coordinates:...
In Exercises 1-10, indicate if the point with the given polar coordinates is represented by A, B, C, or D on the graph. or 90° Tor 180° 0 or 0° B C D or 270 517 1. (3,225) 3. 4. 2. (3,315) 5. (3,7) 8. (3.-315) 6. (-3,0) 37 9. 4 (-3,- 7. (3,-135) 57 10. -3, 4
Draw what the E-field vector (and thus the polarization) looks
like for linearly polarized light, at eight equally-spaced times in
the light's period (i.e. at phase angles 0∘, 45∘, 90∘, 135∘, 180∘,
225∘, 270∘, and 315∘). Include both direction and magnitude (see
figure below).
Repeat this for circularly and elliptically polarized
light.
0。 45° 135 TİME