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IB Mathematics: Applications and Interpretation HL · 12.10: Geometry & Trigonometry · 12.10.10

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Radians and degrees Problem set B

Show the multiplication you use. Give exact answers as multiples of π unless the question asks for a decimal.

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. Fill in the missing entries of this table, writing radians as fractions of π.

    Degrees?300135??315Radians4π/3??7π/6π/3?

  2. Write each angle in radians, as a multiple of π.

    1. (a) −210°
    2. (b) 480°
    3. (c) −495°
    4. (d) 800°

  3. Write each angle in degrees.

    1. (a) \(\frac{3\pi}{10}\)
    2. (b) \(-\frac{11\pi}{4}\)
    3. (c) \(\frac{17\pi}{6}\)
    4. (d) \(-\frac{29\pi}{12}\)

  4. Give each answer to 3 significant figures.

    1. (a) 55° in radians
    2. (b) 3.4 radians in degrees
    3. (c) −2.5 radians in degrees

In context

  1. A record turntable spins through 990°.

    1. (a) Write the angle in radians, as a multiple of π.
    2. (b) How many complete turns is this, as a decimal?

  2. A hamster wheel has radius 12 cm. A sticker on the edge moves 51 cm along the edge. Find

    1. (a) the angle turned, in radians
    2. (b) the angle turned, in degrees (3 s.f.)

  3. The hour hand of a clock moves for 7 hours. Find

    1. (a) the angle in degrees
    2. (b) the angle in radians, in terms of π

Stretch

  1. Write 3.8 radians, \(\frac{7\pi}{6}\) radians and 215° in order, smallest first.

  2. A roundabout turns through −13 radians. Find

    1. (a) the angle in degrees (3 s.f.)
    2. (b) the number of full turns, and the direction

jmaths.xyz · AI HL · 12.10.10 Radians and degrees