Printable · GCSE Foundation · ages 14-16
Exact trigonometric values worksheet — GCSE Foundation
Fifteen questions on "exact trigonometric values" — DfE statement G21. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
Exact trigonometric values worksheet — GCSE Foundation
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- 1.Work out the exact value of tan 30° + tan 30°.
- 2.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.
- 3.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.
- 4.Write down the exact value of sin 60°.
- 5.Write down the exact value of tan 60°.
- 6.Write down the exact value of tan 0°.
- 7.Work out the exact value of cos 0° − sin 30°.
- 8.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.
- 9.Write down the exact value of sin 45°.
- 10.Three of these are rational numbers and one is irrational. Write down the one that is irrational.
- 11.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.
- 12.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.
- 13.Work out the exact value of (sin 30°)² + (cos 30°)².
- 14.Each of these has an exact value. Write down the one whose value is the greatest.
- 15.A pop-up canopy has two sloping supports that meet at the top. Each support makes an angle of 30° with the ground and is 6 m long. Using the exact value of cos 30°, work out the total width of the canopy's base.
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