A __________ is a rule that assigns each value of the independent variable to exactly one value of the dependent variable.
1 answer:
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answer:
(a).
Equation of circle is <u>x²</u><u> </u><u>+</u><u> </u><u>y²</u><u> </u><u>-</u><u> </u><u>2</u><u>5</u><u> </u><u>=</u><u> </u><u>0</u>
(b).
(-5, 0) » yes
(√7, 1) » no
(-3, √21) » no
(0, 7) » no
Step-by-step explanation:
(a).
If centred at origin, centre is (0, 0)
General equation of circle:
but g and f are 0:
The cosine of an angle is the x-coordinate of the point where its terminal ray intersects the unit circle. So, we can draw a line at x=-1/2 and see where it intersects the unit circle. That will tell us possible values of θ/2.
We find that vertical line intersects the unit circle at points where the rays make an angle of ±120° with the positive x-axis. If you consider only positive angles, these angles are 120° = 2π/3 radians, or 240° = 4π/3 radians. Since these are values of θ/2, the corresponding values of θ are double these values.
a) The cosine values repeat every 2π, so the general form of the smallest angle will be
... θ = 2(2π/3 + 2kπ) = 4π/3 + 4kπ
b) Similarly, the values repeat for the larger angle every 2π, so the general form of that is
... θ = 2(4π/3 + 2kπ) = 8π/3 + 4kπ
c) Using these expressions with k=0, 1, 2, we get
... θ = {4π/3, 8π/3, 16π/3, 20π/3, 28π/3, 32π/3}
We see here in the diagram that the base is a. We know this because the height is perpendicular to it. We also know the height is bsin(C) which, when replace h for bsin(C) and a for the base, we get A=absin(C), which is the second option.
