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Access custom-built, exam-style problems for trig equations & identities. Each problem has a full solution and mark-scheme, as well as AI grading and support.
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The depth of water in a harbor, in meters, is modeled by
where t is the number of hours after midnight.
Write down the mean depth of the water.
Find the maximum depth of the water.
Find the depth of the water at 2AM.
State the period of the function and explain what it represents in this context.
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Hugh notices that the average daily temperature T in his town is modeled by
where t is the hours after midnight.
Find the domain of T.
Find the range of T.
Determine the average temperature in Hugh's town when he leaves for work at 8:30 AM.
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The distance of a passenger from the ground on the London Eye ferris wheel, in meters, is given by
where t is how many minutes the passenger has been on the wheel.
Find how far above the ground a passenger is when they board the London Eye.
Calculate the period of rotation of the London Eye.
The dome atop St. Paul's Cathedral is only visible when passengers are at least 111m above the ground.
Determine how long the dome is visible during one rotation of the London Eye.
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The points P and Q lie on a circle with center O and radius r such that PO^Q=2 radians.
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The perimeter of the shaded region is 7π.
Find the value of r.
Hence find the area of the region inside the circle that is not shaded.
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A spherical white blood cell appears as a circle with circumference 6π×10−5m.
Write down the radius of the cell.
Find the volume of the cell, giving your answer in the form π(a×10k)m3, where a<10 and k∈Z.
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The blades of a wind turbine have a diameter of 16m and rotate clockwise at a constant speed, 1 revolution every 4 seconds. The blades are fixed on a shaft such that the tips of the blades are always at least 7m above the ground. The point Q lies at the tip of one of the blades.
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Let h be the height, in meters, of Q above the ground. After t minutes, h is given by h(t)=acos(bt)+c, where a,b,c∈R and a>0.
Show that Q starts at the highest possible point.
Find the values of a, b and c.
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