Question

[1.077(x/y)]^2 + [0.533(x/y)]^2 = 1
Solvable?

Answer 1

Combine like terms?

Answer 2

this question makes no sense

Answer 3

I know, here it is in its original form on the third page:
https://drive.google.com/file/d/0BxRNoTFgXVMzTlE0VnR0c09pQkk/view?usp=sharing

Answer 4

You already asked this question, and I already told you how to answer it:

http://openstudy.com/study#/updates/54d53e7ae4b068f80a122946

Answer 5

it was too vague for me to understand

Answer 6

it'd be better if you could explain how the cos^2x + sin^2x = 1
comes into play

did I apply my professors suggestion wrongly?

Answer 7

she means to "plug in" the values like I started this new post off with right?

Answer 8

OK, I'll explain it in full this time. It's a very common method though so you should learn it:

\[\begin{cases} F_1 a = F_3 \sin x \\ F_1 b = F_3 \cos x \end{cases} \]

We can divide through based on what I stated in the other thread, which gives:

\[\frac{F_1 a}{F_1 b} = \frac{F_3 \sin x}{F_3 \cos x} \implies \frac{a}{b} = \tan x \implies x = \tan^{-1}(a/b) \]

Answer 9

I'll look at the method using s^2 + c^2 = 1 now, but it seems needlessly complicated

Answer 10

ohhhhhhhhhhh, I just blindly used atan before now
THANKS!

Answer 11

The alternate method is OK, I guess. You are right up to where you got to, but you need to divide through by (x/y)^2, then square root, giving sqrt(1.077^2 + 0.533^2) = sqrt((y/x)^2) = y/x.

hence y = sqrt(1.077^2 + 0.533^2) * x

And now you've found F_3 before the angle, so you substitute this back into the either of the original equations and work out the angle. Either method is fine, so pick whichever you find easier

Answer 12

@adamaero It is probably easier to understand the method I used if you take the intermediate step of writing sin and cos in terms of the other terms (as your teacher did). then you can just divide the sin terms by the cos term. The way I do it is slicker, but perhaps less obvious.