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The London Eye is a popular tourist attraction in London, England and is one of the largest Ferris Wheels in the world. It has a diameter of 135 meters and makes one revolution (counterclockwise) every 30 minutes. It is constructed so that the lowest part of the Eye reaches ground level, enabling passengers to simply walk on to, and off of, the ride. Find a sinsuoid which models the height \(h\) of the passenger above the ground in meters \(t\) minutes after they board the Eye at ground level.

Solve for the remaining side(s) and angle(s) if possible. As in the text, \((\alpha, a)\), \((\beta, b)\) and \((\gamma, c)\) are angle-side opposite pairs. \(\alpha=95^{\circ}, \beta=85^{\circ}, a=33.33\)

Plot the graph of the polar equation by hand. Carefully label your graphs. Rose: \(r=\sin (4 \theta)\)

Plot the point given in polar coordinates and then give three different expressions for the point such that (a) \(r<0\) and \(0 \leq \theta \leq 2 \pi\), (b) \(r>0\) and \(\theta \leq 0\) (c) \(r>0\) and \(\theta \geq 2 \pi\) \(\left(-1, \frac{2 \pi}{3}\right)\)

What other things in the world might be roughly sinusoidal? Look to see what models you can find for them and share your results with your class.

Plot the point given in polar coordinates and then give three different expressions for the point such that (a) \(r<0\) and \(0 \leq \theta \leq 2 \pi\), (b) \(r>0\) and \(\theta \leq 0\) (c) \(r>0\) and \(\theta \geq 2 \pi\) \(\left(-3,-\frac{11 \pi}{6}\right)\)

In Exercises \(11-25\), find the component form of the vector \(\vec{v}\) using the information given about its magnitude and direction. Give exact values. \(\|\vec{v}\|=4 ;\) when drawn in standard position \(\vec{v}\) lies in Quadrant II and makes a \(30^{\circ}\) angle with the negative \(x\) -axis

The hour hand on my antique Seth Thomas schoolhouse clock in 4 inches long and the minute hand is 5.5 inches long. Find the distance between the ends of the hands when the clock reads four o'clock. Round your answer to the nearest hundredth of an inch.

Plot the graph of the polar equation by hand. Carefully label your graphs. Lemniscate: \(r^{2}=4 \cos (2 \theta)\)

The HMS Sasquatch leaves port on a bearing of \(\mathrm{N} 23^{\circ} \mathrm{E}\) and travels for 5 miles. It then changes course and follows a heading of \(\mathrm{S} 41^{\circ} \mathrm{E}\) for 2 miles. How far is it from port? Round your answer to the nearest hundredth of a mile. What is its bearing to port? Round your angle to the nearest degree.