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.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.
- 2.Write down the exact value of sin 60°.
- 3.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.
- 4.Write down the exact value of tan 0°.
- 5.Work out the exact value of cos 0° − sin 30°.
- 6.Work out the exact value of sin 30° + cos 60°.
- 7.Write down the exact value of sin 45°.
- 8.Write down the exact value of tan 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 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.
- 11.Work out the exact value of tan 30° + tan 30°.
- 12.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.
- 13.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.
- 14.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.
- 15.Three of these are rational numbers and one is irrational. Write down the one that is irrational.
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