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Year 11 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 hypotenuse is 5 cm. What is the sine of that angle? Give your answer as a fraction.

  3. 3.What is sin 90°?

  4. 4.Match each trigonometric ratio to its value.

    • sin 30°
    • cos 30°
    • tan 45°
    • sin 0°
    • tan 60°
    • 0
    • √3
    • √3/2
    • 1/2
    • 1

  5. 5.In a right-angled triangle the side next to an angle is 4 cm and the hypotenuse is 5 cm. What is the cosine of that angle? Give your answer as a fraction.

  6. 6.What is tan 45°?

  7. 7.What is cos 60°? Give your answer as a fraction.

  8. 8.For any angle θ, what does sin²θ + cos²θ come to?

Answer key — Year 11 Maths — Introduction to trigonometry

  1. 1. 1/2
  2. 2. 3/5
  3. 3. 1
  4. 4. sin 30° → 1/2; cos 30° → √3/2; tan 45° → 1; sin 0° → 0; tan 60° → √3
  5. 5. 4/5
  6. 6. 1
  7. 7. 1/2
  8. 8. 1