Additional Topics in Trigonometry

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Across
  1. 2. In the the complex plane, the vertical axis is referred to as the _?_ axis.
  2. 8. The first step in solving an oblique triangle when only the sides are known is to use the Law of _?_.
  3. 9. The _?_ of two complex numbers in polar form is found by multiplying their moduli and adding their arguments.
  4. 10. In the complex plane, the horizontal axis is referred to as the _?_ axis.
  5. 11. In polar coordinates, the equation r=7sin3Θ has a petal length of _?_.
  6. 12. In polar coordinates, the equation r=5cos4Θ has _?_ petals.
  7. 14. The _?_ of two complex numbers in polar form is found by dividing their moduli and subtracting their arguments.
  8. 15. _?_ a triangle means finding the lengths of its sides and measurements of its sides.
  9. 16. _?_ formula can be used to find the area of a triangle when all three sides are known.
  10. 17. If v=<a,b> is an algebraic vector whose initial point is the origin, the v is called a(n) _?_ vector.
  11. 18. In polar coordinates, the graphs of r=a±bcosΘ and r=a±bsinΘ are called _?_ if a=b.
  12. 23. In polar coordinates, the graphs of r=a±bcosΘ and r=a±bsinΘ are called _?_ if a>0 and b>0..
  13. 24. The positive x-axis in rectangular coordinates coincides with the _?_ _?_ in polar coordinates.
  14. 26. A quantity that has magnitude but no direction is called a/an _?_.
  15. 28. In polar coordinates, the graphs of r=acosnΘ or r=asinΘ are called _?_ _?_.
  16. 30. The _?_ component of a nonzero vector can be found by multiplying its magnitude and the sine of the direction angle.
  17. 31. If v and w are two nonzero vectors and Θ is the smallest nonnegative angle between them, then the dot product equals the product of the magnitudes times the _?_ of Θ.
Down
  1. 1. If the dot product of two vectors is 0, then the two vectors are _?_.
  2. 3. The _?_ of v=ai+bj is given by ||v||=√(a²+b²)
  3. 4. The area of a triangle can be found by taking half of the product of two side and the _?_ of the included angle.
  4. 5. The value √(a²+b²) is the _?_ _?_ of the complex number a+bi.
  5. 6. A _?_ is a quantity with magnitude and direction.
  6. 7. For any nonzero vector v, the _?_ _?_ that has the same direction as v is found by dividing v by its magnitude.
  7. 13. In polar coordinates, the graphs of r²=a²sin2Θ and r²=a²cos2Θ are shaped like propellers and called _?_.
  8. 19. If v=ai+bj and w=ci+dj are vectors, the _?_ _?_ of the two vectors is defined as ac+bd.
  9. 20. The _?_ component of a nonzero vector can be found be multiplying its magnitude and the cosine of the direction angle.
  10. 21. A triangle that does not contain a right angle is called a/an _?_ triangle.
  11. 22. The origin in rectangular coordinates coincides with the _?_ in polar coordinates.
  12. 25. In polar coordinates, the graphs of r=a±bcosΘ and r=a±bsinΘ are limaçons with a _?_ if a<b.
  13. 27. In polar coordinates, the graphs of r=acosΘ and r=asinΘ are _?_.
  14. 29. The possibility of two triangles arises when the first step of solving a triangle is finding an angle with the Law of _?_.