SOLUTION: r = 4 cos(6𝜃) Identify zeros of r, 0 ≤ 𝜃 ≤ 2𝜋. Use a graphing utility to verify your results. (Enter your answers as a comma-separated list.)

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Question 1177441: r = 4 cos(6𝜃)
Identify zeros of r, 0 ≤ 𝜃 ≤ 2𝜋. Use a graphing utility to verify your results. (Enter your answers as a comma-separated list.)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!


Identify zeros of ,
To find the zeros, set equal to zero and solve for theta.












intercepts:
(,),(,),(,),(,),(,),(,),(,),(,),(,)


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Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!





On the interval 0 to 2pi, cosine theta is 0 twice -- at pi/2 and 3pi/2. Cosine of 6*theta will be 0 6*2=12 times on that interval; the first two zeros will be at (pi/2)/6 and (3pi/2)/6, or pi/12 and 3pi/12. Of course you might want to simplify that second zero to pi/4, but that's not absolutely necessary.

The separation between successive zeros of cosine theta is pi; the separation between zeros of cosine of 6*theta is pi/6 or 2pi/12.

The zeros of on the interval 0 to 2pi:

pi/12, 3pi/12, 5pi/12,..., 19pi/12, 21pi/12, 23pi/12
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