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r=8cos⁡(θ)r = 8\cos(\theta)

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Determine the direction of a vector scalar multipleright chevron icon

Full solution

Q. r=8cos⁡(θ)r = 8\cos(\theta)
  1. Set equation and solve: To find the points where the curve intersects the x-axis, we need to set rr equal to 00 and solve for θ\theta.0=8cos⁡(θ)0 = 8\cos(\theta)
  2. Isolate cos⁡(θ)\cos(\theta): Divide both sides by 88 to isolate cos⁡(θ)\cos(\theta).\newline08=cos⁡(θ)\frac{0}{8} = \cos(\theta)\newlinecos⁡(θ)=0\cos(\theta) = 0
  3. Find theta values: Find the values of theta where the cosine function equals 00.\newlinecos⁡(θ)=0\cos(\theta) = 0 at θ=π2\theta = \frac{\pi}{2} and 3π2\frac{3\pi}{2}
  4. Convert theta to points: Convert the values of theta back into points on the curve using the polar coordinate system.\newlineFor θ=π2\theta = \frac{\pi}{2}, r=8cos⁡(π2)=8(0)=0r = 8\cos(\frac{\pi}{2}) = 8(0) = 0\newlineFor θ=3π2\theta = \frac{3\pi}{2}, r=8cos⁡(3π2)=8(0)=0r = 8\cos(\frac{3\pi}{2}) = 8(0) = 0
  5. Intersecting points: The points where the curve intersects the x-axis are at (0,π2)(0, \frac{\pi}{2}) and (0,3π2)(0, \frac{3\pi}{2}).

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