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Trigonometric Functions and the Unit Circle: math test, Grade 12 – download the PDF

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Math tests Grade 12 : Trigonometric Functions and the Unit Circle — Zyro the alien explorer of Planète Maths

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

1 Radians and arcs / 4 pts

a) Convert \(210^\circ\) to radians. b) Convert \(\dfrac{11\pi}{4}\) to degrees. c) Find the arc length of a sector of radius \(9\text{ in}\) and central angle \(\dfrac{2\pi}{3}\). d) Find the exact area of that sector.

2 Exact values / 4 pts

Give the exact value (no calculator): a) \(\sin\dfrac{5\pi}{3}\) b) \(\cos\dfrac{3\pi}{4}\) c) \(\tan\dfrac{7\pi}{6}\) d) \(\sec\dfrac{11\pi}{6}\) (rationalize).

3 Using the Pythagorean identity / 3 pts

Suppose \(\cos\theta=-\dfrac{8}{17}\) and \(\theta\) is in quadrant III. Find \(\sin\theta\), \(\tan\theta\) and \(\csc\theta\).

4 A ladder (calculator allowed) / 3 pts

A \(4.5\text{ m}\) ladder makes a \(64^\circ\) angle with the ground. Draw a sketch, then find how high the ladder reaches and how far its foot is from the wall, to the nearest hundredth of a meter.

5 Solving an equation / 3 pts

Solve \(2\cos\theta+1=0\) for \(0\le\theta<2\pi\).

6 Wind turbine (calculator allowed) / 3 pts

A wind turbine blade is \(120\text{ ft}\) long and the rotor turns at \(15\) rpm. Find the angular velocity in radians per minute, the speed of the blade tip in feet per minute, and that speed in miles per hour (\(1\text{ mi}=5280\text{ ft}\)), to the nearest tenth.

See the test solutions : Trigonometric Functions and the Unit Circle: math test, Grade 12 – Planète Maths

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