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Year 10 Maths — Introduction to trigonometry

Find sine, cosine and tangent in a right-angled triangle and recall the standard angles.

Name: ________________________

Before you start

One angle of this right-angled triangle has been marked. Find out what that angle and each of the three sides are called.

1234
  1. 1. Opposite
  2. 2. Adjacent
  3. 3. Hypotenuse
  4. 4. The marked angle

Mark the other corner instead and opposite and adjacent swap over. The hypotenuse never moves, because it is fixed by the right angle rather than by the angle you chose.

  1. 1.What is sin 30°? Give your answer as a fraction.

  2. 2.In a right-angled triangle the side opposite an angle is 3 cm and the side next to it is 4 cm. What is the tangent of that angle? Give your answer as a fraction.

  3. 3.What is tan 45°?

  4. 4.What is tan 30°?

    • a) 1/2
    • b) 1/√3
    • c) √3
    • d) √3/2

  5. 5.What is sin 60°?

    • a) 1/√3
    • b) 1/2
    • c) √3
    • d) √3/2

  6. 6.What is sin 90°?

  7. 7.What is cos 0°?

  8. 8.Sort each ratio by its value.

    Groups: Equals 0 · Equals 1

    • tan 0°
    • cos 90°
    • cos 0°
    • sin 90°
    • sin 0°
    • tan 45°

Answer key — Year 10 Maths — Introduction to trigonometry

  1. 1. 1/2
  2. 2. 3/4
  3. 3. 1
  4. 4. b) 1/√3
  5. 5. d) √3/2
  6. 6. 1
  7. 7. 1
  8. 8. sin 0° → Equals 0; cos 90° → Equals 0; tan 0° → Equals 0; cos 0° → Equals 1; sin 90° → Equals 1; tan 45° → Equals 1