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.Each of these has an exact value. Write down the one whose value is the greatest.
- 2.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.
- 3.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.
- 4.Write down the exact value of cos 30°.
- 5.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.
- 6.Write down the exact value of cos 45°.
- 7.Write down the exact value of sin 45°.
- 8.Write down the exact value of tan 60°.
- 9.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.
- 10.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.
- 11.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.
- 12.Work out the exact value of cos 0° − sin 30°.
- 13.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.
- 14.Work out the exact value of (cos 45°)² + (sin 45°)².
- 15.Work out the exact value of (sin 30°)² + (cos 30°)².
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