Precalculus/Trigonometry Chapter 8 Practice Quiz

Precalculus/Trigonometry Chapter 8 Practice QuizPlot and label the following points given in polar coordinates.1. A( 2, 330 )⎛ π ⎞2. D⎜−3, ⎟⎝ 3 ⎠⎛ π ⎞3. C ⎜3,− ⎟⎝ 3 ⎠4. B( −4,60 )A point is graphed in polar coordinates. Name the same point four different ways.5. ( + _____, + _____)( + _____, − _____)( − _____, + _____)( −_____, − _____)6. The rectangular points of a point are given. Find the polar coordinates of each point. [Use your chartfor (a) and calculator for (b). Remember you can use the R P in the angle menu](a) ( − 3,3)(______, ______)(b) ( 8.3, 4.2 )(______, ______)7. The polar coordinates of a point are given. Find the rectangular coordinates of each point. [Use yourchart for (a) and calculator for (b). Remember you can use the P R in the angle menu](a) ( 5, 300 )(______, ______)(b) ( 6.3, 3.8 )(______, ______)

Identify the following polar equations by matching.L. lemniscate 8. _____ r = 2 − 2cosθM. rose with five petalsN. rose with four petals 9. _____ r = 4sin( 5θ)O. limacon without inner loopP. limacon with inner loop 10. _____ r = 1−3cosθQ. cardioidR. circle 11. _____2r = sin( 2θ)S. vertical lineT. horizontal lineWrite the complex numbers in polar form. Express the argument in degrees.2 2x + yi r = x + y r cosθ+ i sinθ( )12. 2+ 3i____________Write the complex number in rectangular form.⎛ 3π3π⎞13. 3⎜cos + isin⎟⎝ 2 2 ⎠____________Find zw and z w ( ) ( )z = 2 cos80 + isin80 , w= 6 cos 200 + isin 20014. zw ___________________ 15.zw___________________Write the expression in the standard form a + bi.16. ⎡ ( ) ⎤3⎣3 cos80 + isin80⎦___________________Find all the complex roots. Leave your answers in polar form with the argument in degrees.17.43 − i____________________________________________________________________________________________________

Use the vectors in the figure to graph each of the following vectors.u w v21. u+v 22. w-vThe vector v has initial point P and terminal point Q. Write v in the form ai + bj; that is, find its positionvector.23. P ( 0,0 ), Q ( 3, 5)= = − − _______________________Find each quantity if v=− 2i+ 3j w= 4i+7j24. v 25. 3v−2w____________________________________________Find the unit vector having the same direction as v.26) v=− 4i+ 3j______________________Write the vector v in the form ai + bj, given its magnitude v and the angle α it makes with thepositive x-axis.27) v = 3 and α = 240______________________