Homework 9

Directions:

  1. Show each step of your work and fully simplify each expression.
  2. Turn in your answers in class on a physical piece of paper.
  3. Staple multiple sheets together.
  4. Feel free to use Desmos for graphing.

Answer the following:

  1. Solve the following equations for $\theta$. Remember to use identities if necessary.
    1. $\sin^2\theta = 4 - 2\cos^2\theta$
    2. $\cos\theta - \sin\theta = 1$
    3. $\csc^2\theta = \cot \theta + 3$
    4. $2 \tan \theta + \sec^2 \theta = 4$
    5. $3\sin 2\theta - 2\sin \theta = 0$
    6. $2\cos 3\theta = 1$
    7. $\tan \dfrac{\theta}{4} + \sqrt{3} = 0$
  2. Plot the point $(4, \pi / 4)$.
  3. Convert these polar coordinates to rectangular coordinates:
    1. $(6, 2\pi/3)$
    2. $(\sqrt{3}, -5\pi/3)$
    3. $(5, 5\pi)$
    4. $(6\sqrt{2}, 11\pi/6)$
  4. Convert these rectangular coordinates to polar:
    1. $(\sqrt{8}, \sqrt{8})$
    2. $(3\sqrt{3}, -3)$
    3. $(-6,0)$
    4. $(0, -\sqrt{3})$
  5. Convert these equations into polar form:
    1. $y=x$
    2. $x^2 + y^2 = 9$
    3. $x = 4$
    4. $y = 5$
  6. Convert these polar equations into rectangular form:
    1. $r = 7$
    2. $r = \dfrac{1}{\sin \theta -\cos \theta}$
    3. $r = 6\cos \theta$
    4. $r = \dfrac{1}{1 + \sin \theta}$
    5. $r\cos \theta = 6$