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.
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Exact trigonometric values worksheet — GCSE Foundation
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- 1.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.
- 2.Work out the exact value of sin 45° × cos 45°.
- 3.Three of these are rational numbers and one is irrational. Write down the one that is irrational.
- 4.Each of these has an exact value. Write down the one whose value is the greatest.
- 5.Work out the exact value of tan 30° + tan 30°.
- 6.Write down the exact value of sin 60°.
- 7.Write down the exact value of cos 30°.
- 8.Write down the exact value of sin 45°.
- 9.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.
- 10.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.
- 11.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.
- 12.Write down the exact value of tan 45°.
- 13.Work out the exact value of (cos 45°)² + (sin 45°)².
- 14.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.
- 15.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.
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