First: Equations are solved.
is an expression, and expressions can be simplified.
Now suppose
. Imagine a right triangle with one angle (not the one opposite the hypotenuse, of course) labeled
. This relation suggests that
![\sin y=\dfrac x2](https://tex.z-dn.net/?f=%5Csin%20y%3D%5Cdfrac%20x2)
and under the hood, we're assuming that
, because otherwise we wouldn't be able to properly alternate from
to
so seamlessly.
Now,
![\tan\left(\sin^{-1}\dfrac x2\right)=\tan y](https://tex.z-dn.net/?f=%5Ctan%5Cleft%28%5Csin%5E%7B-1%7D%5Cdfrac%20x2%5Cright%29%3D%5Ctan%20y)
so the given expression is the same as the tangent of that same angle
.
If
, then in the triangle, the leg opposite the angle
occurs with the length of the hypotenuse in a ratio of
to 2. By the Pythagorean theorem, the remaining side - call it
- satisifies
![z^2+x^2=2^2\implies z=\sqrt{4-x^2}](https://tex.z-dn.net/?f=z%5E2%2Bx%5E2%3D2%5E2%5Cimplies%20z%3D%5Csqrt%7B4-x%5E2%7D)
and we have
![\tan y=\dfrac xz=\dfrac x{\sqrt{4-x^2}}](https://tex.z-dn.net/?f=%5Ctan%20y%3D%5Cdfrac%20xz%3D%5Cdfrac%20x%7B%5Csqrt%7B4-x%5E2%7D%7D)
Answer:
(1,5) (2,3) (-2,-3)
Step-by-step explanation:
When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x,y) to (-y,x) and graph the rotated figure.
Answer:
x=-6
Step-by-step explanation:
2x+1=-x-5
3x+1=-5
3x=-6
x=-2
Answer:
54
Step-by-step explanation:
81*36/54
Answer:
bumhole
Step-by-step explanation:
bumbumbumwnwbnsnjsvhs