In need of some math help(trig/calc)?

Question

Hello there, if anyone would be kind enough to help me out on these problems...maybe steer me in the right direction I would appreciate it. I am confused because our teacher said "no calculators," and I dont see how you can do these without one...

#1) Find all (A) in the interval [0,360) that satisfy the equation.

: 2cosAtanA + tanA =0

-------------answers: 0, 120, 180, 240

#2) Rewrite the given equation using the substitution x= rcosA and y=rsinA. Simplify your answer.

:x^2+y^2+3x=0

Answer: r = -3cosA

#3) In which of the following equations is y a function of x?

a)3x+2y-7=0

b)5x^2y=9-2x

c)3x^2-4y^2=9

d)x=3y^2-1

e) none of these

answer: A and B (How do you know if the equations are a function of x?)

#4) Determine whether the function is even, odd, or neither. Justify your answer:

:f(x)= -x^5+3x^3-2x+1....I plugged in (-x) and I thought it would be "odd" because the equation changed but the answer was : "neither"

I appreciate all of the input you guys give me. I really want to understand how to do these problems, not just asking for answers. Please explain or maybe do 1 example so I can do the rest myself. I thank you for your helpful efforts. Thank you!

Answer 1

[Here is the first one, for now.]

1.)

First, try to simplify as most as possible.

2 cosx tanx + tanx = 0

2 cosx sins/cosx + sinx/cosx = 0

2 sinx + sinx/cosx = 0

(2 sinx cosx + sinx)/cosx = 0

Now, take the numerator and solve for that:

2 sinx cosx + sinx = 0

2 sinx cosx = -sinx

2 cosx = -1

cosx = -1/2

x = 120°, 240°

Now check the denominator (cosx) that it doesn't equal 0, and it obviously does not, so your answer is 120° & 240°. (Though I don't know why 0° and 180°.  Sorry.)

Answer 2

3 is d =]

is because the y and x varibles are sepertated and in A and B they are not they are on the same side of the equation.

thats all i know =[ not very good at math sorry