Given that the radius of the Ferris wheel planned for Alphapark is 70m and that 𝜃 represents the angle measured anti-clockwise from the x-axis, there are different angles for which the pod P is 30m from the x-axis.
Question
Given that the radius of the Ferris wheel planned for Alphapark is 70m and that 𝜃 represents the angle measured anti-clockwise from the x-axis, there are different angles for which the pod P is 30m from the x-axis.
Solution
The problem seems to be about trigonometry and the unit circle. Here's how you can solve it:
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First, we need to understand the problem. We have a Ferris wheel with a radius of 70m. A pod P on the Ferris wheel is 30m from the x-axis. We need to find the angles at which this happens.
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The height of the pod P from the x-axis can be represented as r*sin(𝜃), where r is the radius of the Ferris wheel and 𝜃 is the angle measured anti-clockwise from the x-axis.
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We know that the height is 30m and the radius is 70m. So we can set up the equation 70*sin(𝜃) = 30.
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To solve for 𝜃, we can divide both sides by 70 to get sin(𝜃) = 30/70 = 0.42857.
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Now we can find the angle 𝜃 by taking the inverse sine (also known as arcsin) of 0.42857. Using a calculator, arcsin(0.42857) ≈ 25.38 degrees.
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However, since the sine function has a period of 180 degrees, there is another angle in the unit circle where sin(𝜃) = 0.42857. This angle is 180 - 25.38 = 154.62 degrees.
So, the two angles for which the pod P is 30m from the x-axis are approximately 25.38 degrees and 154.62 degrees.
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