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

Name Date

Radians and degrees Problem set A

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

Difficulty: first skills applying them stretch

Skills

  1. Copy and complete the table. Give radians as multiples of π.

    Degrees150210??315?Radians??5π/411π/6?2π/3

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

    1. (a) −150°
    2. (b) 420°
    3. (c) −585°
    4. (d) 1000°

  3. Write each angle in degrees.

    1. (a) \(\frac{2\pi}{5}\)
    2. (b) \(-\frac{7\pi}{4}\)
    3. (c) \(\frac{13\pi}{3}\)
    4. (d) \(-\frac{31\pi}{12}\)

  4. Give each answer to 3 significant figures.

    1. (a) 75° in radians
    2. (b) 2.1 radians in degrees
    3. (c) −4 radians in degrees

In context

  1. A fairground wheel turns through 1170°.

    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 cyclist's wheel has radius 35 cm. A mark on the rim moves 98 cm along the rim. Find

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

  3. The minute hand of a clock moves for 25 minutes. Find

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

Stretch

  1. Write 220°, 3.9 radians and \(\frac{6\pi}{5}\) radians in order, smallest first.

  2. A turntable turns through −7.5 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