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.Write down the exact value of sin 45°.
- 2.Work out the exact value of sin 45° × cos 45°.
- 3.Work out the exact value of (cos 45°)² + (sin 45°)².
- 4.Write down the exact value of cos 30°.
- 5.A zip-wire is fixed at an angle of 60° to the horizontal ground. The zip-wire is 12 m long. Using the exact value of cos 60°, work out the exact horizontal distance it covers.
- 6.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.
- 7.Write down the exact value of tan 60°.
- 8.Each of these has an exact value. Write down the one whose value is the greatest.
- 9.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.
- 10.Work out the exact value of (sin 30°)² + (cos 30°)².
- 11.A tent's sloping side makes an angle of 45° with the ground. The sloping side is 3√2 m long. Using the exact value of sin 45°, work out the exact height of the tent.
- 12.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.
- 13.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.
- 14.Write down the exact value of cos 45°.
- 15.Write down the exact value of sin 60°.
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