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Trigonometric Functions and the Unit Circle: math test, Grade 11 – download the PDF

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Math tests Grade 11 : 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 degrees / 3 pts

Convert, giving exact answers.

  1. \(72^\circ\) to radians.
  2. \(\dfrac{5\pi}{12}\) radians to degrees.
  3. \(\dfrac{7\pi}{9}\) radians to degrees.

2 Exact values / 4 pts

Give the exact value, without a calculator.

  1. \(\sin\dfrac{2\pi}{3}\)
  2. \(\cos\dfrac{7\pi}{6}\)
  3. \(\tan\dfrac{5\pi}{4}\)
  4. \(\sin\left(-\dfrac{\pi}{6}\right)\)

3 Using the identity / 3 pts

The angle \(\theta\) lies in quadrant III and \(\sin\theta=-\dfrac{8}{17}\).

  1. Find \(\cos\theta\), and justify its sign.
  2. Find \(\tan\theta\).

4 Reading a sinusoid / 3 pts

Consider \(y=2\sin(4x-\pi)+3\).

  1. Rewrite it as \(y=A\sin\big(B(x-C)\big)+D\).
  2. Give the amplitude, the period, the phase shift and the midline.
  3. Give the maximum and minimum values.

5 Equations / 3 pts

Solve on \([0,2\pi)\).

  1. \(2\sin x=\sqrt{3}\)
  2. \(2\cos^2x+\cos x-1=0\)

6 A floating buoy / 4 pts

The height in meters of a buoy above the sea floor is \(h(t)=2+1.5\sin\dfrac{\pi t}{5}\), where \(t\) is in seconds. A calculator is allowed for part (d).

  1. Find the period, the maximum height and the minimum height.
  2. Find \(h(2.5)\).
  3. Solve \(h(t)=2\) for \(0\le t\le10\).
  4. Convert the maximum height to feet to the nearest hundredth (1 ft = 0.3048 m).
See the test solutions : Trigonometric Functions and the Unit Circle: math test, Grade 11 – Planète Maths

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