For 4x^2 - 4xy + y^2 = 4 find θ, the angle of rotation about the origin, to the nearest degree?
a) 27°
b) 63°
c) 333°
d) 307°
I got A, is this right?
I had -26.6 or 333.4 in a positive direction
tan 2θ = B/(A-C)
= -4/(4-1) = -4/3
2θ = -53.13
θ = -26.13
oh, so it is C?
has to be
didn't you also get -26.6 degrees?
that is not given.
What angle is coterminal with -26.6 ?
It is 333.4 .
Here is a webpage that has your type of question
http://education.yahoo.com/homework_help/math_help/problem?id=miniprecalcgt_8_1_1_26_70
press "STEP" to go through the problem.
Notice they leave their angle as a negative.
oohh yes i did! thanks!!
To find the angle of rotation about the origin for the given equation, you can follow these steps:
Step 1: Rewrite the equation in the standard form of a conic section:
Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
Comparing this to the given equation 4x^2 - 4xy + y^2 = 4:
A = 4, B = -4, C = 1, D = 0, E = 0, F = -4.
Step 2: Use the formula to find the angle of rotation:
θ = 0.5 * arctan(B / (A - C))
Plugging in the values, we get:
θ = 0.5 * arctan(-4 / (4 - 1))
θ = 0.5 * arctan(-4 / 3)
Step 3: Calculate the value of θ using a calculator:
θ ≈ -31.062°
Since the given options are in positive degrees, we take the absolute value of θ:
θ ≈ 31.062°
Now, let's check which option is the closest to 31.062°.
a) 27° -> This is the closest option to 31.062°.
b) 63° -> This option is farther from 31.062°.
c) 333° -> This option is farther from 31.062°.
d) 307° -> This option is farther from 31.062°.
Therefore, the closest option to the angle of rotation about the origin is A) 27°.
So, your answer A is incorrect.