Idk if it's clear, but it's sqrt2/2 divided by -sqrt2/2
#Small thing, but not sure how to solve this. :)
toxic pawn
soft sphinxBOT
Idk if it's clear, but it's sqrt2/2 divided by -sqrt2/2
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small fjord
$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}$
barren cliffBOT
Romans 12:19
small fjord
or in this case, let $\frac{\sqrt{2}}{2}=u$ then we have $\frac{u}{-u}=-1$
barren cliffBOT
Romans 12:19
toxic pawn
so that comes out to be (sqrt2 * 2)/(2 * -sqrt2), would I cancel out the 2's? 🤔
small fjord
so that comes out to be (sqrt2 * 2)/(2 * -sqrt2), would I cancel out the 2's? 🤔
yes, and cancel out a sqrt(2) as well
toxic pawn
Oh. Then what am I left with?
small fjord
-1
small fjord
it's simply asking for which angles between $0$ and $2\pi$ for which $\cos x=-\frac{\sqrt{2}}{2}$ and $\sin x=\frac{\sqrt{2}}{2}$
barren cliffBOT
Romans 12:19
small fjord
do u know when sinx=sqrt(2)/2
toxic pawn
I don't think so? I might've been taught but forgot
small fjord
do u know what sin(pi/4) is
toxic pawn
I wrote that down somewhere, hold on
toxic pawn
oop np
whole lion
One sec, let me move to my PC.
toxic pawn
it's no biggie if you aren't available, for this specific one I can go to tutoring if needed in a few days :)
whole lion
second one
Alright. So, are you trying to solve this one?
whole lion
Well, in any case, here's how you do it:
The points on a unit circle have coordinates (cos(θ), sin(θ)). So:
- Identify the signs of cos(θ) and sin(θ). That will determine the quarter that θ is in.
- Find tan(θ) = sin(θ)/cos(θ), then find θ in the quarter that you determined before.
For example, in (I) we have:
cos(θ) = 1/2 > 0
sin(θ) = √(3)/2 > 0
So, the angle is in the first quarter. Next:
tan(θ) = √(3)
θ = π/3 + πn, n ∈ ℤ
The value lying in the first quarter is θ = π/3. If that's not immediately visible, we can solve a double inequality:
0 ≤ π/3 + πn ≤ π/2
0 ≤ 1/3 + n ≤ 1/2
-1/3 ≤ n ≤ 1/6
The integer solution is n = 0, so θ = π/3.
toxic pawn
Well, in any case, here's how you do it:
The points on a unit circle have coordi...
that's what I was tryna do before, but got -1 D: