Exploring the graph of y equals cosine Theta
1 answer:
Answer: see below
<u>Step-by-step explanation:</u>
The coordinates on the Unit Circle are (cos, sin). Since we are focused on cosine, we only need to focus on the left side of the coordinate. The cosine value (left side) will be the y-value of the function y = cos x
Use the quadrangles (angles on the axes) to represent the x-values of the function y = cos x.
Quadrangles are: 0°, 90°, 180°, 270°, 360° <em>(360° = 0°)</em>
Together, the coordinates will be as follow:
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4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.
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We have , so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.
Taken mod 7, the first and last terms vanish and we're left with
which is what we want, so no adjustments needed here.
Taken mod 9, the first two terms vanish and we're left with
so we don't need to make any adjustments here, and we end up with .
By the Chinese remainder theorem, we find that any such that
is a solution to this system, i.e. for any integer
, the smallest and positive of which is 149.