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Trigonometry test 1

Answer the following questions:

  1. Convert the following angles to radians:

    1. \(60^\circ\)
    2. \(12^\circ15'\)
    3. \(-225^\circ\)

  2. Convert the following angles from radians to degrees (Use \(\pi=\frac{22}{7}\)):

    1. \(3.5\)
    2. \(-\frac{3\pi}{10}\)
    3. \(\frac{5\pi}{9}\)

  3. In 2 circles, same angle \(\theta\) creates arcs of lengths \(15\,cm\) and \(25\,cm\). Find the ratio of the radii of the circles.

  4. A car is travelling at a speed of \(25\,m/s\). If the radius of the wheel is \(50\,cm\), then how many radians does the wheel rotate in \(1\,s\)?

    Hint

    For 1 revolution of the car, the distance travelled is the circumference of the wheel.

  5. Find the signs of each of the given trigonometric ratio, in the specified quadrant.

    1. \(\sin{\theta}\), in \(3^{rd}\) quadrant
    2. \(\sec{\theta}\), in \(4^{th}\) quadrant
    3. \(\cot{\theta}\), in \(2^{th}\) quadrant

  6. Give the values of following trigonometric ratios:

    1. \(\sin{60^\circ}\)
    2. \(\tan{45^\circ}\)
    3. \(\cot{\frac{\pi}{2}}\)
    4. \(\text{cosec}\,{\frac{5\pi}{3}}\)
    5. \(\cos{855^\circ}\)

  7. If \(\tan{\theta}=\frac{5}{12}\) and \(\theta\) is in \(3^{rd}\) quadrant, then find the values of all trigonometric ratios.